Motion

Meaning of Motion

An object is said to be in motion if its position changes with time relative to a fixed reference point.

To describe motion accurately, Physics uses five key quantities:

• distance,

• displacement,

• speed,

• velocity,

• acceleration.

These quantities form the foundation for all later topics in kinematics.

Distance

Distance is defined as:

The total length of the path travelled by an object, regardless of direction.

Key characteristics:

• It is a scalar quantity (has magnitude only).

• It is always positive.

• SI unit: metre (m).

Example:

If a student walks 5 m east and then 3 m west, the total distance travelled is 8 m.

Displacement

Displacement is defined as:

The straight-line distance from the initial position to the final position, measured in a specified direction.

Key characteristics:

• It is a vector quantity (has magnitude and direction).

• It can be positive, negative, or zero.

• SI unit: metre (m).

Example:

For the same movement (5 m east, then 3 m west), the displacement is 2 m east.

Speed

Speed is defined as:

The distance travelled per unit time.

Key characteristics:

• Scalar quantity.

• Indicates how fast an object is moving.

• SI unit: metre per second (m s).

Speed does not give information about direction.

Velocity

Velocity is defined as:

The rate of change of displacement with time.

Key characteristics:

• Vector quantity.

• Includes direction.

• SI unit: metre per second (m s).

An object moving at constant speed can still have changing velocity if its direction changes.

Acceleration

Acceleration is defined as:

The rate of change of velocity with time.

Key characteristics:

• Vector quantity.

• Occurs when:
  • speed increases,
  • speed decreases,
  • direction changes.

• SI unit: metre per second squared (m s).

Scalar and Vector Classification (Exam-Focused)

This distinction is frequently tested in Paper 1 and Paper 2.

Examination Errors

Students often:

• confuse distance with displacement,

• define velocity as speed,

• forget to mention direction in vector definitions,

• write incorrect SI units (e.g. m/s² for velocity).

Clear definitions earn easy marks in examinations.

Questions

Question 1

Define distance and displacement.

Question 2

State one difference between speed and velocity.

Question 3

A car travels 10 m east and then 6 m west in 4 s.

(a) Calculate the distance travelled.

(b) Determine the displacement.

Question 4

Define acceleration.

Solutions

Solution 1

• Distance is the total length of the path travelled by an object.

• Displacement is the straight-line distance from the starting point to the final position in a given direction.

Solution 2

Speed has magnitude only, while velocity has both magnitude and direction.

Solution 3

(a)

(b)

Solution 4

Acceleration is the rate of change of velocity with time.

End-of-Objective

A learner who has mastered this objective can:

• correctly define motion quantities,

• distinguish between scalar and vector quantities,

• apply definitions to simple motion scenarios,

• use correct SI units and scientific language.

Why Equations Are Used in Motion

Motion involves quantities that are mathematically related. Equations allow physicists to:

• predict motion,

• compare different motions,

• analyse experimental results.

Correct use of equations is essential for Paper 1 (objective questions) and Paper 2 (structured problems).

Equation for Speed

Speed is the distance travelled per unit time.

Where:

• speed is measured in m s,

• distance in metres (m),

• time in seconds (s).

Rearrangements:

Equation for Velocity

Velocity is the displacement per unit time.

Important:

• Direction must be stated where necessary.

• SI unit remains m s.

Equation for Acceleration

Acceleration is the rate of change of velocity.

Where:

• u = initial velocity,

• v = final velocity,

• t = time,

• a = acceleration (m s⁻²).

Acceleration can be:

• positive (speeding up),

• negative (slowing down / deceleration),

• zero (constant velocity).

Using Units Correctly (Exam-Critical)

Before substitution:

• convert time into seconds,

• convert distance into metres,

• ensure velocity is in m s.

Failure to convert units is one of the most common causes of lost marks.

Motion Relationships (Conceptual Support)

Understanding equations is easier when motion is visualised.

From a distance–time graph:

• speed = gradient of the graph

From a velocity–time graph:

• acceleration = gradient of the graph

(These links strengthen understanding but calculations remain equation-based at this level.)

Step-by-Step Problem-Solving Strategy

When solving motion problems:

1. Write down the given values.

2. Select the correct equation.

3. Substitute values with correct units.

4. Calculate carefully.

5. State the answer with unit and direction where required.

Examination Errors

Students often:

• use distance instead of displacement,

• forget to convert minutes to seconds,

• omit units in final answers,

• mix up symbols u, v, and a.

Clear working earns method marks, even if the final answer is wrong.

Questions

Question 1

State the equation used to calculate speed.

Question 2

A cyclist travels 240 m in 30 s.

Calculate the speed of the cyclist.

Question 3

A car accelerates from rest to 20 m s in 5 s.

Calculate the acceleration of the car.

Question 4

A runner moves with a constant velocity of 4 m s for 12 s.

Determine the distance travelled.

Solutions

Solution 1

Solution 2

Solution 3

Given:

• $u = 0\,\text{m s}$

• $v = 20\,\text{m s}$

• $t = 5\,\text{s}$

Solution 4

End-of-Objective

A learner who has mastered this objective can:

• apply motion equations correctly,

• rearrange equations confidently,

• convert units accurately,

• solve motion problems with clear, logical steps.

Understanding Velocity in Motion

Velocity describes how an object’s displacement changes with time and includes direction.

When analysing motion, it is essential to determine whether velocity:

• remains constant, or

• changes with time.

This distinction leads to uniform and non-uniform velocity.

Uniform Velocity

An object is said to move with uniform velocity if:

Its velocity remains constant throughout the motion.

This means:

• the object covers equal displacements in equal time intervals,

• both speed and direction remain unchanged,

• acceleration is zero.

Examples:

• A car moving in a straight line at constant speed,

• A conveyor belt moving steadily in one direction.

From the velocity–time graph:

• a horizontal line indicates constant velocity,

• slope (acceleration) = 0.

Non-Uniform Velocity

An object is said to move with non-uniform velocity if:

Its velocity changes with time, either in magnitude, direction, or both.

This occurs when:

• speed increases or decreases,

• direction of motion changes,

• acceleration is not zero.

Examples:

• A car accelerating from rest,

• A cyclist slowing down,

• Circular motion at constant speed but changing direction.

From the velocity–time graph:

• a sloping line indicates changing velocity,

• slope represents acceleration.

Graphical Identification (Exam-Critical Skill)

Motion type can be identified using graphs:

Velocity–Time Graphs

• Uniform velocity → straight horizontal line

• Non-uniform velocity → sloping or curved line

Distance–Time Graphs

• Uniform velocity → straight line with constant gradient

• Non-uniform velocity → curved line with changing gradient

Summary Comparison (Concept Consolidation)

This comparison is frequently assessed in Paper 1 and Paper 2.

Examination Errors

Students often:

• confuse uniform velocity with constant speed (ignoring direction),

• identify motion only from words without using graphs,

• assume straight-line motion is always uniform,

• misinterpret curved distance–time graphs.

Clear interpretation earns easy marks.

Questions

Question 1

Define uniform velocity.

Question 2

State one condition under which motion is non-uniform.

Question 3

A car travels equal distances in equal intervals of time in a straight line.

Identify the type of velocity and give a reason for your answer.

Question 4

A velocity–time graph shows a straight line sloping upwards.

(a) Identify the type of velocity.

(b) State whether acceleration is present.

Solutions

Solution 1

Uniform velocity is motion in which an object’s velocity remains constant, meaning both speed and direction do not change with time.

Solution 2

Motion is non-uniform when the velocity changes with time, either due to a change in speed or direction.

Solution 3

The velocity is uniform because the object covers equal distances in equal time intervals in the same direction.

Solution 4

(a) The velocity is non-uniform.

(b) Acceleration is present because the velocity changes with time.

End-of-Objective

A learner who has mastered this objective can:

• distinguish uniform from non-uniform velocity,

• identify motion type using graphs,

• explain velocity changes using clear scientific reasoning,

• apply concepts to real-life motion situations.

Understanding Acceleration in Motion

Acceleration describes how velocity changes with time.

When analysing motion, it is important to determine whether this change:

• happens at a constant rate, or

• varies from moment to moment.

This leads to uniformly accelerated and non-uniformly accelerated motion.

Uniformly Accelerated Motion

An object is said to be in uniformly accelerated motion if:

Its acceleration remains constant throughout the motion.

This means:

• velocity changes by equal amounts in equal time intervals,

• acceleration has a constant value,

• motion equations such as $v = u + at$ apply.

Examples:

• A car accelerating steadily from rest,

• An object falling freely under gravity (near the Earth’s surface, ignoring air resistance).

From the velocity–time graph:

• straight sloping line → uniform acceleration,

• gradient = acceleration (constant).

Non-Uniformly Accelerated Motion

An object is said to be in non-uniformly accelerated motion if:

Its acceleration changes with time.

This means:

• velocity does not change evenly,

• acceleration is not constant,

• simple linear motion equations do not directly apply.

Examples:

• A car moving in traffic (frequent braking and speeding up),

• A falling object experiencing air resistance,

• A vehicle moving on a rough or uneven surface.

From the velocity–time graph:

• curved line → non-uniform acceleration,

• gradient changes with time.

Identifying Acceleration from Graphs (Exam-Critical)

Velocity–Time Graphs

• Uniform acceleration → straight line

• Non-uniform acceleration → curved line

Distance–Time Graphs

• Uniform acceleration → curve with steadily increasing gradient

• Non-uniform acceleration → irregular curve

Summary Comparison (Concept Consolidation)

This comparison is frequently tested in Paper 1 and Paper 2.

Examination Errors

Students often:

• confuse non-uniform velocity with non-uniform acceleration,

• assume any curved graph always represents acceleration,

• fail to interpret gradients correctly,

• describe graphs without linking them to acceleration.

Clear identification and explanation earn high-confidence marks.

Questions

Question 1

Define uniformly accelerated motion.

Question 2

State one feature of non-uniformly accelerated motion.

Question 3

A velocity–time graph is a straight line sloping upwards.

(a) Identify the type of acceleration.

(b) State whether the acceleration is constant or changing.

Question 4

A car’s velocity–time graph is curved.

What does this indicate about the car’s acceleration?

Solutions

Solution 1

Uniformly accelerated motion is motion in which acceleration remains constant, causing velocity to change by equal amounts in equal time intervals.

Solution 2

In non-uniformly accelerated motion, the acceleration changes with time.

Solution 3

(a) The motion shows uniform acceleration.

(b) The acceleration is constant, since the graph is a straight line.

Solution 4

The curved velocity–time graph indicates that the car’s acceleration is changing with time, meaning the motion is non-uniformly accelerated.

End-of-Objective

A learner who has mastered this objective can:

• distinguish uniform from non-uniform acceleration,

• identify acceleration type from graphs,

• explain velocity changes using scientific reasoning,

• relate acceleration behaviour to real-life motion.

Why Graphs Are Used in Motion

Graphs provide a visual representation of motion, making it easier to:

• analyse how motion changes with time,

• compare different motions,

• extract quantitative information such as speed.

In examinations, graph questions test both conceptual understanding and data-handling skills.

Distance–Time Graphs for Uniform Motion

A distance–time graph shows how the distance travelled by an object changes with time.

For uniform motion:

• the object covers equal distances in equal time intervals,

• speed is constant.

This produces a straight-line graph.

Interpreting a Distance–Time Graph

From a distance–time graph:

• the gradient (slope) represents the speed of the object,

• a steeper line indicates a higher speed,

• a horizontal line indicates the object is at rest.

For uniform motion, the gradient is constant throughout.

Plotting a Distance–Time Graph (Exam Skill)

To plot a correct graph:

1. Choose suitable scales for both axes.

2. Label axes with quantity and unit.

3. Plot points accurately.

4. Draw a best-fit straight line through the points.

Failure to label axes correctly results in lost marks.

Speed–Time Graphs for Uniform Motion

A speed–time graph shows how speed changes with time.

For uniform motion:

• speed remains constant,

• the graph is a horizontal straight line above the time axis.

Interpreting a Speed–Time Graph

From a speed–time graph:

• the height of the line represents the speed,

• the area under the graph represents the distance travelled.

For uniform motion:

This reinforces the speed equation visually.

Comparison of the Two Graphs (Concept Link)

Understanding both graphs strengthens overall motion analysis.

Examination Errors

Students often:

• draw curved lines for uniform motion,

• forget to label axes or units,

• confuse gradient with area,

• interpret speed–time graphs as distance–time graphs.

Accurate plotting and correct interpretation are high-mark opportunities.

Questions

Question 1

Describe the shape of a distance–time graph for uniform motion.

Question 2

A distance–time graph is a straight line with a constant gradient.

What does this indicate about the motion of the object?

Question 3

An object moves with a constant speed of 5 m s for 8 s.

(a) Sketch the speed–time graph.

(b) Calculate the distance travelled.

Question 4

Explain how speed can be determined from a distance–time graph.

Solutions

Solution 1

The distance–time graph for uniform motion is a straight line, indicating constant speed.

Solution 2

The straight-line distance–time graph shows that the object moves with uniform motion, covering equal distances in equal time intervals.

Solution 3

(a)

(b)

Solution 4

Speed is determined from a distance–time graph by calculating the gradient, which is the change in distance divided by the change in time.

End-of-Objective

A learner who has mastered this objective can:

• plot accurate motion graphs,

• interpret gradients and areas correctly,

• link graphs to motion equations,

• explain uniform motion using graphical evidence.

Meaning of Non-Uniform Motion

Non-uniform motion occurs when:

• speed changes with time, or

• direction changes, or

• acceleration is not constant.

In such motion, an object does not cover equal distances in equal time intervals.

Graphical representation is the clearest way to identify and analyse this type of motion.

Distance–Time Graphs for Non-Uniform Motion

A distance–time graph for non-uniform motion is curved, not straight.

This is because:

• the gradient (speed) changes with time,

• the object may be accelerating or decelerating.

Interpreting a Distance–Time Graph (Non-Uniform Motion)

From a curved distance–time graph:

• Gradient at any point represents the instantaneous speed.

• Increasing gradient → speed is increasing (acceleration).

• Decreasing gradient → speed is decreasing (deceleration).

• Horizontal section → object is at rest.

This interpretation is essential for Paper 2 structured questions.

Plotting Distance–Time Graphs (Exam Skill)

To plot a distance–time graph for non-uniform motion:

1. Choose suitable scales for time and distance.

2. Plot all given data points accurately.

3. Draw a smooth curve, not straight line segments.

4. Label axes clearly with quantities and units.

Speed–Time Graphs for Non-Uniform Motion

A speed–time graph for non-uniform motion is not horizontal.

Depending on how speed changes:

• straight sloping line → uniform acceleration,

• curved line → non-uniform acceleration.

Interpreting a Speed–Time Graph (Non-Uniform Motion)

From a speed–time graph:

• Gradient represents acceleration.

• Changing gradient → acceleration is changing.

• Area under the graph represents distance travelled.

For curved graphs:

• distance must be estimated using counting squares or approximation methods.

Comparing Uniform and Non-Uniform Motion Graphs

This comparison is frequently tested in Paper 1 multiple-choice questions.

Examination Errors

Students often:

• draw straight lines instead of curves for non-uniform motion,

• confuse gradient with area,

• fail to interpret changing gradient correctly,

• forget to state units on axes.

Clear graph shape recognition earns high-confidence marks.

Questions

Question 1

Describe the shape of a distance–time graph for non-uniform motion.

Question 2

A distance–time graph becomes steeper with time.

What does this indicate about the motion of the object?

Question 3

A speed–time graph is curved.

(a) What does the gradient of the graph represent?

(b) What does the changing gradient indicate?

Question 4

Explain how the distance travelled can be determined from a speed–time graph for non-uniform motion.

Solutions

Solution 1

The distance–time graph for non-uniform motion is curved, showing that speed changes with time.

Solution 2

The increasing steepness indicates that the speed of the object is increasing, meaning the object is accelerating.

Solution 3

(a) The gradient represents acceleration.

(b) The changing gradient indicates that acceleration is not constant.

Solution 4

The distance travelled is found by calculating the area under the speed–time graph. For curved graphs, this area is estimated using suitable approximation methods.

End-of-Objective

A learner who has mastered this objective can:

• plot accurate graphs for changing motion,

• interpret gradients and areas correctly,

• distinguish uniform from non-uniform motion graphically,

• explain motion behaviour using scientific language.

Conditions for Using the Equations of Motion

The equations of motion apply when:

• motion is along a straight line,

• acceleration is constant (uniform acceleration),

• motion variables change smoothly with time.

The Three Equations of Motion

The standard equations used at BGCSE level are:

1. Velocity–time equation

1. Displacement–time equation

1. Velocity–displacement equation

Where:

• u = initial velocity (m s),

• v = final velocity (m s),

• a = acceleration (m s),

• t = time (s),

• s = displacement (m).

Choosing the Correct Equation (Exam Strategy)

To select the correct equation:

1. List the known quantities.

2. Identify the unknown quantity.

3. Choose the equation that includes only one unknown.

This method avoids unnecessary algebra and reduces errors.

Physical Meaning of Each Equation

• $v = u + at$
  Shows how velocity changes with time under constant acceleration.

• $s = ut + \tfrac{1}{2}at^2$
  Calculates displacement when acceleration is present.

• $v^2 = u^2 + 2as$
  Used when time is not given.

Understanding meaning prevents blind substitution.

Graphical Support (Conceptual Link)

The equations of motion are linked to velocity–time graphs.

• Gradient = acceleration a

• Area under graph = displacement s

Units and Sign Convention (Exam-Critical)

• Always use SI units.

• Choose a positive direction and keep it consistent.

• Negative acceleration indicates deceleration.

Incorrect sign usage is a frequent cause of lost marks.

Examination Errors

Students often:

• apply equations to non-uniform acceleration,

• confuse displacement with distance,

• forget to square velocity or time correctly,

• omit units in final answers.

Clear working earns method marks even if the final answer is incorrect.

Questions

Question 1

State one condition under which the equations of motion can be used.

Question 2

A car accelerates uniformly from rest at 2 m s for 6 s.

Calculate the final velocity of the car.

Question 3

An object moving with an initial velocity of 5 m s accelerates uniformly at 3 m s for 4 s.

Calculate the displacement.

Question 4

A body accelerates uniformly from 4 m s to 20 m s over a distance of 96 m.

Calculate the acceleration.

Solutions

Solution 1

The equations of motion can be used when acceleration is constant and motion is along a straight line.

Solution 2

Given:

• u = 0

• a = 2 m s

• t = 6 s

Solution 3

Given:

• u = 5 m s

• a = 3 m s

• t = 4 s

Solution 4

Given:

• u = 4 m s

• v = 20 m s

• s = 96 m

End-of-Objective

A learner who has mastered this objective can:

• identify when to use motion equations,

• select the correct equation efficiently,

• solve problems clearly and accurately,

• interpret answers physically and mathematically.

Meaning of Acceleration Due to Gravity

The symbol g represents the acceleration due to gravity.

Acceleration due to gravity is defined as:

The constant acceleration with which an object falls freely towards the Earth when air resistance is negligible.

This acceleration is caused by the gravitational pull of the Earth on objects.

Value of g

Near the Earth’s surface:

For most BGCSE calculations, this value may be:

• taken as 9.8 m s, or

• approximated to 10 m s where stated or appropriate.

The SI unit of g is metre per second squared (m s).

Direction of g

Acceleration due to gravity always acts:

• vertically downwards,

• towards the centre of the Earth.

This direction is important when applying sign conventions in motion equations.

Free Fall and g

An object is said to be in free fall when:

• gravity is the only force acting on it,

• effects of air resistance are negligible.

In free fall:

• all objects accelerate at the same rate g,

• mass of the object does not affect the value of g.

This explains why, in theory, a stone and a feather fall together in a vacuum.

g as a Special Case of Acceleration

Acceleration due to gravity is a specific example of uniform acceleration because:

• its magnitude is constant near the Earth’s surface,

• it can be used directly in the equations of motion.

When an object is falling freely:

• acceleration a = g,

• motion equations can be applied with a replaced by g.

Difference Between g and Weight (Concept Clarification)

• g is an acceleration.

• Weight is a force given by:

Confusing these two leads to frequent examination errors.

Examination Errors

Students often:

• define g as a force instead of an acceleration,

• give incorrect units for g,

• confuse g with mass or weight,

• forget to state the direction of g.

Clear definition earns easy marks.

Questions

Question 1

Define acceleration due to gravity.

Question 2

State the SI unit of acceleration due to gravity.

Question 3

An object is released from rest and falls freely near the Earth’s surface.

State the value of its acceleration and give its direction.

Solutions

Solution 1

Acceleration due to gravity is the constant acceleration with which an object falls towards the Earth when gravity is the only force acting on it.

Solution 2

The SI unit of acceleration due to gravity is metre per second squared (m s).

Solution 3

The acceleration is 9.8 m s, acting vertically downwards towards the centre of the Earth.

End-of-Objective

A learner who has mastered this objective can:

• correctly define g,

• state its value and unit,

• explain its direction,

• apply it appropriately in motion calculations.

Role of g in Motion Problems

When an object moves vertically under the influence of gravity alone, its acceleration is equal to the acceleration due to gravity, g.

In such cases:

• acceleration is constant,

• equations of motion can be applied,

• horizontal motion equations do not apply directly.

Choosing the Direction and Sign Convention

Before solving problems involving g, a sign convention must be chosen.

Common convention:

• Upwards is positive

• Downwards is negative

Under this convention:

• acceleration due to gravity:

Using a consistent sign convention is essential for correct answers.

Using g in the Equations of Motion

The standard equations of motion are used, with:

Depending on direction chosen.

Equations:

Where:

• $a = g$ or a = -g,

• $g = 9.8\,\text{m s}$ (or $10\,\text{m s}$ where stated).

Freely Falling Objects

For an object released from rest:

• initial velocity u = 0,

• acceleration $a = g$ (downwards).

This simplifies calculations and is frequently tested.

Object Thrown Vertically Upwards

When an object is thrown upwards:

• initial velocity is upwards,

• acceleration due to gravity acts downwards,

• velocity decreases until it becomes zero at the highest point.

At the highest point:

Typical Motion Scenarios Using g

Recognising these conditions simplifies problem-solving.

Step-by-Step Problem-Solving Strategy

1. Draw a simple motion sketch.

2. Choose and state a sign convention.

3. List known values.

4. Select the appropriate equation.

5. Substitute values carefully.

6. State final answer with unit and direction if required.

Examination Errors

Students often:

• use the wrong sign for g,

• forget that acceleration acts even when an object is moving upward,

• fail to state units,

• confuse distance with displacement.

Careful setup earns method marks.

Questions

Question 1

An object is released from rest and falls freely for 4 s.

Calculate the velocity of the object after 4 s.

(Take g = 9.8 m s.)

Question 2

A ball is thrown vertically upwards with an initial velocity of 20 m s.

Calculate the time taken for the ball to reach its maximum height.

(Take g = 10 m s.)

Question 3

A stone is dropped from a height and reaches the ground with a velocity of 14 m s.

Calculate the height from which it was dropped.

(Take g = 9.8 m s.)

Solutions

Solution 1

Given:

• $u = 0$

• $a = 9.8\,\text{m s}^{-2}$

• $t = 4\,\text{s}$

Velocity after 4 s = 39.2 m s downward.

Solution 2

Given:

• $u = 20\,\text{m s}$

• $v = 0$

• $a = -10\,\text{m s}^{-2}$

Time to reach maximum height = 2 s.

Solution 3

Given:

• $u = 0$

• $v = 14\,\text{m s}$

• $a = 9.8\,\text{m s}^{-2}$

Height = 10 m.

End-of-Objective

A learner who has mastered this objective can:

• recognise motion under gravity,

• apply g correctly in equations of motion calculations,

• solve vertical motion problems confidently,

• interpret results with correct units and direction.

Meaning of Free Fall

A body is said to be in free fall when:

• it is moving under the influence of gravity only, and

• air resistance is negligible.

In free fall, gravity is the only force acting on the object.

Constant Acceleration in Free Fall

Near the Earth’s surface, the acceleration of a freely falling body is:

• constant, and

• equal to the acceleration due to gravity, denoted by g.

This means that:

• the velocity of the object changes by equal amounts in equal time intervals,

• the motion is an example of uniformly accelerated motion.

For some calculations, g may be taken as 10 m s if stated.

Direction of the Acceleration

The acceleration due to gravity:

• always acts vertically downward,

• towards the centre of the Earth.

This direction remains the same whether the object is:

• falling downward, or

• thrown upward.

Why Acceleration Is Constant Near the Earth

Near the Earth’s surface:

• the gravitational field strength is approximately uniform,

• changes in height are very small compared to the Earth’s radius.

As a result, the gravitational force — and therefore the acceleration — remains effectively constant for everyday motion.

Conditions for the Statement to Be True (Exam Clarity)

The statement “acceleration of free fall is constant” is valid when:

• motion occurs near the Earth’s surface,

• air resistance is ignored or negligible,

• the height involved is not extremely large.

If air resistance is significant, acceleration is not constant.

Experimental Evidence (Conceptual Link)

Experiments show that:

• heavy and light objects fall with the same acceleration in the absence of air resistance,

• differences observed in air are due to drag, not gravity.

This supports the idea that free-fall acceleration is constant.

Examination Errors

Students often:

• state the acceleration is constant without mentioning free fall,

• forget to specify “near the Earth’s surface”,

• confuse constant acceleration with constant velocity,

• include air resistance incorrectly.

Precise wording earns full marks.

Questions

Question 1

State what is meant by free fall.

Question 2

State the acceleration of a body in free fall near the Earth’s surface.

Question 3

Explain why the acceleration of free fall near the Earth can be considered constant.

Solutions

Solution 1

Free fall is motion in which a body moves under the influence of gravity only, with air resistance neglected.

Solution 2

The acceleration of a body in free fall near the Earth’s surface is constant and equal to $g \approx 9.8\,\text{m s}$.

Solution 3

Near the Earth’s surface, the gravitational field strength is approximately uniform, and changes in height are small compared to the Earth’s radius. Therefore, the gravitational force — and hence the acceleration — remains constant.

End-of-Objective

A learner who has mastered this objective can:

• state that free-fall acceleration is constant,

• explain the conditions under which this applies,

• distinguish between constant acceleration and constant velocity,

• use correct scientific language and units.

Forces Acting on a Body Falling in Air

When a body falls through air, two main forces act on it:

1. Weight (gravitational force) – acts vertically downward.

2. Air resistance (drag) – acts upward, opposing the motion.

Because air resistance is present, the motion differs from ideal free fall in a vacuum.

Initial Stage of the Fall

At the moment the body is released:

• its velocity is zero,

• air resistance is negligible (very small),

• the only significant force is weight.

As a result:

• the body accelerates downward at a value close to g.

Increasing Speed and Air Resistance

As the body falls:

• its speed increases,

• air resistance increases because it depends on speed,

• the upward air resistance begins to reduce the net downward force.

Consequences:

• acceleration decreases from its initial value,

• velocity continues to increase, but at a slower rate.

Terminal Velocity

Eventually, the body reaches a speed at which:

• air resistance equals the weight of the body,

• the resultant force becomes zero.

At this point:

• acceleration becomes zero,

• the body continues to fall at a constant speed called terminal velocity.

Motion Summary in Stages

The motion of a body freely falling in air can be summarised in three stages:

Factors Affecting Motion in Air

Terminal velocity and falling behaviour depend on:

• shape of the object,

• surface area,

• mass,

• density of air.

For example:

• a flat sheet of paper falls slower than a crumpled one,

• a parachute greatly increases air resistance.

Comparison with Free Fall in a Vacuum (Concept Clarification)

Understanding this comparison prevents conceptual errors in exams.

Examination Errors

Students often:

• state that acceleration is always equal to g in air,

• confuse terminal velocity with maximum velocity,

• forget that acceleration becomes zero at terminal velocity,

• ignore the role of air resistance.

Clear stage-by-stage description earns full marks.

Questions

Question 1

Name the two forces acting on a body falling through air.

Question 2

Describe how the acceleration of a body falling in air changes as its speed increases.

Question 3

Explain why a falling body eventually reaches a constant speed in air.

Solutions

Solution 1

The two forces acting are weight (gravity) acting downward and air resistance acting upward.

Solution 2

As the speed increases, air resistance increases, reducing the resultant downward force. This causes the acceleration to decrease from its initial value until it becomes zero.

Solution 3

A body reaches a constant speed when air resistance becomes equal to its weight. At this point, the resultant force is zero, so acceleration is zero and the body continues to fall at terminal velocity.

End-of-Objective

A learner who has mastered this objective can:

• describe falling motion in air in correct stages,

• explain the role of air resistance,

• distinguish between motion in air and in a vacuum,

• use correct scientific terminology such as terminal velocity.

Forces Acting on an Object Falling in a Liquid

When an object falls through a liquid (such as water or oil), three forces act on it:

1. Weight – acts vertically downward due to gravity.

2. Upthrust (buoyant force) – acts upward due to displacement of liquid.

3. Liquid resistance (viscous drag) – acts upward, opposing motion.

Initial Stage of Motion in a Liquid

At the moment the object is released:

• its velocity is zero,

• liquid resistance is negligible,

• upthrust is present but constant,

• the resultant force acts downward.

As a result:

• the object accelerates downward.

Increasing Speed and Liquid Resistance

As the object falls:

• its speed increases,

• liquid resistance increases rapidly (liquids offer much greater resistance than air),

• the upward forces (upthrust + liquid resistance) increase.

Consequences:

• the resultant downward force decreases,

• acceleration reduces gradually.

Terminal Velocity in a Liquid

Eventually, a point is reached where:

• weight = upthrust + liquid resistance,

• the resultant force becomes zero.

At this stage:

• acceleration becomes zero,

• the object falls with a constant speed known as terminal velocity.

In liquids, terminal velocity is:

• reached quickly,

• usually much smaller than in air.

Comparison: Falling in Air vs Falling in a Liquid

This comparison is frequently assessed qualitatively in exams.

Factors Affecting Motion in a Liquid

The motion of an object falling in a liquid depends on:

• viscosity of the liquid (thicker liquids provide more resistance),

• shape and surface area of the object,

• mass and density of the object.

Example:

• A steel ball falls faster in water than a plastic ball of the same size.

• The same object falls slower in oil than in water.

Qualitative Description Summary (Exam Language)

A correct qualitative description should include:

• forces acting,

• change in acceleration,

• existence of terminal velocity,

• comparison with falling in air.

Using clear stages earns full descriptive marks.

Examination Errors

Students often:

• forget to include upthrust,

• state that acceleration is constant in a liquid,

• confuse terminal velocity with maximum speed,

• describe motion without mentioning forces.

Precise scientific language is essential.

Questions

Question 1

Name two forces acting on an object falling in a liquid.

Question 2

Describe how the acceleration of an object changes as it falls through a liquid.

Question 3

Explain why an object falling in a liquid reaches terminal velocity more quickly than in air.

Solutions

Solution 1

Two forces are weight acting downward and liquid resistance acting upward. (Upthrust also acts upward.)

Solution 2

Initially, the object accelerates downward. As its speed increases, liquid resistance increases, reducing the resultant force. This causes acceleration to decrease until it becomes zero at terminal velocity.

Solution 3

Liquids provide much greater resistance than air. As a result, the upward resistive force increases quickly, causing the resultant force to become zero sooner. This makes the object reach terminal velocity more quickly in a liquid.

End-of-Objective

A learner who has mastered this objective can:

• describe motion in a liquid using correct stages,

• identify all forces acting on a falling object,

• explain terminal velocity qualitatively,

• compare motion in air and in liquids clearly.

Meaning of Terminal Velocity

Terminal velocity is defined as:

The constant maximum speed attained by an object falling through a fluid (air or liquid) when the resultant force acting on it becomes zero.

At terminal velocity:

• the object continues to move,

• its speed remains constant,

• its acceleration is zero.

Forces Involved in Terminal Velocity

When an object falls through a fluid, the following forces act:

• Weight (downward),

• Resistive force (air resistance or liquid resistance, upward),

• Upthrust (upward, significant in liquids).

Terminal velocity is reached when:

That is:

• in air: weight = air resistance,

• in liquid: weight = air/liquid resistance + upthrust.

How Terminal Velocity Is Reached (Step-by-Step Description)

1. At release
   • Speed is zero.
   • Resistive force is negligible.
   • Resultant force acts downward.
   • Object accelerates.

2. As speed increases
   • Resistive force increases.
   • Resultant downward force decreases.
   • Acceleration reduces.

3. At terminal velocity
   • Resistive force equals weight (and upthrust if in a liquid).
   • Resultant force is zero.
   • Acceleration becomes zero.
   • Speed becomes constant.

Terminal Velocity and Acceleration (Key Clarification)

• Terminal velocity does not mean zero velocity.

• It means zero acceleration.

This distinction is critical in examinations.

Factors Affecting Terminal Velocity

Terminal velocity depends on:

• mass of the object,

• surface area and shape of the object,

• density and viscosity of the fluid.

Examples:

• A skydiver reaches a higher terminal velocity than a feather.

• A parachute reduces terminal velocity by increasing surface area.

• Objects reach lower terminal velocities in liquids than in air.

Terminal Velocity in Air vs in a Liquid

This comparison is frequently assessed qualitatively.

Examination Errors

Students often:

• state that motion stops at terminal velocity,

• confuse terminal velocity with maximum velocity in free fall,

• forget to mention balanced forces,

• say acceleration is equal to g at terminal velocity.

Precise language earns full definition marks.

Questions

Question 1

Define terminal velocity.

Question 2

State the value of acceleration when an object is moving at terminal velocity.

Question 3

Explain why an object falling through air eventually reaches terminal velocity.

Solutions

Solution 1

Terminal velocity is the constant maximum speed reached by a falling object when the resistive forces equal the weight, resulting in zero resultant force.

Solution 2

The acceleration is zero.

Solution 3

As the object falls, air resistance increases with speed. Eventually, air resistance becomes equal to the weight of the object, making the resultant force zero. With no resultant force, acceleration becomes zero and the object continues to fall at constant speed, known as terminal velocity.

End-of-Objective

A learner who has mastered this objective can:

• define terminal velocity precisely,

• explain how it is reached using forces,

• distinguish between zero velocity and zero acceleration,

• apply the concept to motion in air and liquids.