Forces and motion

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Distance and Displacement

Distance is how far an object moves, regardless of direction. It is a scalar quantity.
Displacement is the straight-line distance from start to finish, together with the direction. It is a vector quantity.
For example, in a 300 m race on a 400 m track, the distance run is 300 m, but the displacement might be 100 m to the right of the start.
If a runner completes a full 400 m lap, the distance is 400 m but the displacement is zero.
Scalars have magnitude only; vectors have both magnitude and direction.
Common scalar–vector pairs: distance/displacement, speed/velocity, mass/weight.

Distance vs displacement

Speed and Velocity

Speed is the distance travelled per second. It is a scalar quantity (no direction).
Velocity is speed in a given direction. It is a vector quantity.
For constant speed: speed = distance ÷ time (v = s/t).
For non-uniform motion, use average speed = total distance ÷ total time.
Typical speeds: walking ~1.5 m/s, running ~3 m/s, cycling ~6 m/s.
The speed of sound in air is typically 330 m/s; in seawater it is about 1500 m/s.
Speed of a moving object is rarely constant; factors affecting walking/running/cycling speed include age, terrain, fitness and distance.

Comparing speed and velocity

Distance–Time Graphs

A distance–time graph shows how distance from a starting point changes with time.
A straight line represents constant speed; the steeper the line, the greater the speed.
A flat horizontal line means the object is stationary.
A curve represents changing speed: increasing gradient means acceleration, decreasing gradient means deceleration.
The speed is equal to the gradient of the line: speed = Δy / Δx.
To find speed at a specific time on a curve, draw a tangent and calculate its gradient.

Gradient of a distance-time graph

Acceleration

Acceleration is the rate of change of velocity: a = Δv / t.
Change in velocity: Δv = final velocity − initial velocity (v − u).
Units: acceleration in m/s², velocity in m/s, time in s.
Positive acceleration means speeding up; negative acceleration (deceleration) means slowing down.
Typical accelerations: a family car takes about 10 s to reach 27 m/s, giving ~2.7 m/s².
Near Earth's surface, free fall acceleration due to gravity is about 9.8 m/s² (often approximated as 10 m/s²).

Illustration of positive and negative acceleration with a rocket and a car.

Velocity–Time Graphs

A velocity–time graph shows how velocity changes with time.
A straight line represents constant acceleration; the steeper the line, the greater the acceleration.
A flat horizontal line means zero acceleration (constant velocity).
Acceleration is the gradient of a velocity–time graph: a = Δy / Δx.
The area under a velocity–time graph gives the distance travelled (or displacement).
For a triangle, area = ½ × base × height; for a rectangle, area = base × height.
If the area is complex, count squares under the graph to estimate distance.

The area under a speed-time graph, split into a triangle and a rectangle (base × height), gives the distance travelled.

Uniform Acceleration Equation

For uniform (constant) acceleration: v² − u² = 2 × a × s.
v = final speed (m/s), u = initial speed (m/s), a = acceleration (m/s²), s = distance (m).
Use this equation when time is not known.
Example: a car accelerates from rest at 2.5 m/s² to 16 m/s. Distance = (16² − 0²) / (2 × 2.5) = 51.2 m.

Newton's Laws and Forces

Newton's First Law: if the resultant force on an object is zero, a stationary object stays stationary and a moving object continues at the same speed and direction (constant velocity).
A resultant force is needed to change an object's velocity (speed and/or direction).
When a vehicle travels at steady speed, the driving force and resistive forces are balanced.
Inertia is the tendency of an object to continue in its state of rest or uniform motion.
Newton's Second Law: resultant force = mass × acceleration (F = ma).
Newton's Third Law: for every action, there is an equal and opposite reaction.

A free-body diagram: two applied forces (F1, F2), friction, and weight drawn as arrows from a central point representing the object.

Terminal Velocity

An object falling through a fluid initially accelerates due to gravity.
As speed increases, air resistance (drag) increases.
Eventually, the upward drag equals the downward weight, so the resultant force is zero.
At this point the object moves at its terminal velocity — constant speed.
At terminal velocity, forces are balanced, but they are not zero; the object still moves.

A speed-time graph for a skydiver: air resistance builds as speed increases until it balances weight and a constant (terminal) velocity is reached.

Forces and Braking

Stopping distance = thinking distance + braking distance.
Thinking distance is the distance travelled during the driver's reaction time. It depends on speed and reaction time (affected by tiredness, alcohol, distractions).
Braking distance is the distance travelled while the brakes are applied. It depends on speed, road conditions, tyre and brake condition.
Reaction distance = speed × reaction time.
For a given braking force, increasing speed increases braking distance because kinetic energy is proportional to speed squared.
Work done by brakes = kinetic energy = ½ × mass × speed².
Braking force × braking distance = work done (energy transferred).

Measuring Speed and Practical Skills

To measure speed, time how long an object takes to travel a known distance, then use speed = distance ÷ time.
Choose appropriate equipment: metre rule for short distances, tape measure or trundle wheel for long distances.
Light gates give more accurate timing: a flag on the object blocks a beam, starting and stopping a timer.
A single light gate can measure speed if the flag length (distance) and blocking time are known.
When describing an experiment, write the equation first to identify which quantities to measure.

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1.Which of the following is a scalar quantity?
Easy
- AVelocity
- BDisplacement
- CSpeed
- DAcceleration
2.A student walks 300 m around a running track and finishes 100 m to the right of the start. Which statement is correct?
Easy
- AThe distance travelled is 100 m and the displacement is 300 m to the right
- BThe distance travelled is 300 m and the displacement is 100 m to the right
- CBoth the distance and the displacement are 300 m
- DBoth the distance and the displacement are 100 m to the right
3.Velocity is a vector quantity because it describes both speed and direction.
Easy
True or false?
4.Which of the following are vector quantities? (Select all that apply)
Medium
- ADistance
- BDisplacement
- CSpeed
- DVelocity
- EAcceleration
5.The equation relating speed, distance and time is speed = distance ÷ time. A plane flies at an average speed of 250 m/s for 2 hours. What is the total distance travelled?
Medium
- A500 m
- B30 000 m
- C1 800 000 m
- D9000 m
6.The gradient of a distance-time graph represents which quantity?
Medium
- AAcceleration
- BSpeed
- CDisplacement
- DForce
7.Which statement correctly describes acceleration?
Medium
- AAcceleration is the rate of change of distance
- BAcceleration is the rate of change of velocity
- CAcceleration is the total distance travelled per second
- DAcceleration is the rate of change of force
8.A Japanese bullet train decelerates at a constant rate in a straight line. Its velocity decreases from 50 m/s to 42 m/s in 30 seconds. What is the train's acceleration?
Medium
- A-0.27 m/s²
- B0.27 m/s²
- C-8 m/s²
- D-1.6 m/s²

Plus de questions

9.A car accelerates steadily from rest at 2.5 m/s² up to a speed of 16 m/s. How far does the car move during this period of acceleration?
Medium
- A25.6 m
- B51.2 m
- C102.4 m
- D5.1 m
10.On a velocity-time graph, a flat horizontal line means the object is accelerating.
Easy
True or false?
11.The area under a velocity-time graph represents which quantity?
Hard
- AAcceleration
- BDistance travelled (or displacement)
- CSpeed
- DForce
12.Match each quantity to whether it is a scalar or a vector.
Medium
- Distance
- Displacement
- Speed
- Velocity
- Scalar
- Vector
13.Which of the following are scalar quantities? (Select all that apply)
Medium
- ADistance
- BDisplacement
- CSpeed
- DVelocity
- EMass
14.Order these quantities from purely scalar to fully vector, starting with the scalar quantity that has no direction at all and ending with the vector that describes speed in a given direction.
Medium
- Distance
- Speed
- Velocity
15.An athlete runs one complete lap of a 400 m circular track and returns to the starting point. Which statement about the athlete's motion is correct?
Medium
- ADistance travelled is 400 m and displacement is 0 m
- BDistance travelled is 0 m and displacement is 400 m
- CDistance travelled is 400 m and displacement is 400 m
- DDistance travelled is 0 m and displacement is 0 m
16.A car travels 60 km due north and then 60 km due south. Which statement is correct?
Medium
- ADistance travelled is 120 km and displacement is 0 km
- BDistance travelled is 0 km and displacement is 120 km
- CDistance travelled is 120 km and displacement is 120 km
- DDistance travelled is 60 km and displacement is 0 km
17.A cyclist rides at a constant speed around a circular track. Which statement is correct?
Hard
- AThe speed is constant but the velocity is changing
- BBoth speed and velocity are constant
- CThe speed is changing but the velocity is constant
- DBoth speed and velocity are changing
18.A car is travelling at a constant speed of 20 m/s along a straight road. Which of the following statements are correct? (Select all that apply)
Medium
- AThe car's velocity is constant
- BThe car is accelerating
- CThe resultant force on the car is zero
- DThe car's speed is changing
- EThe car's direction is constant
19.A car's velocity changes from 4 m/s to 24 m/s in 5 seconds. What is its acceleration?
Medium
- A4 m/s²
- B5 m/s²
- C20 m/s²
- D0.2 m/s²
20.A cyclist is travelling at 12 m/s and decelerates at 3 m/s². How long does it take the cyclist to stop?
Hard
- A4 s
- B9 s
- C36 s
- D0.25 s
21.On a distance-time graph, what does a flat horizontal line represent?
Medium
- AThe object is stationary
- BThe object is moving at constant speed
- CThe object is accelerating
- DThe object is decelerating
22.A distance-time graph shows a straight line rising to 90 m in 15 s. What is the object's speed?
Medium
- A6 m/s
- B90 m/s
- C0.17 m/s
- D1350 m/s
23.Which of the following are shown by the gradient of a distance-time graph? (Select all that apply)
Medium
- AThe speed of the object
- BHow far the object has travelled
- CWhether the object is stationary
- DThe acceleration of the object
- EWhether the object is moving at a constant speed
24.On a velocity-time graph, what does a flat horizontal line represent?
Medium
- AThe object is moving at a constant velocity
- BThe object is stationary
- CThe object is accelerating
- DThe object is decelerating
25.A velocity-time graph shows a line rising from 0 m/s to 20 m/s over 8 seconds. What is the acceleration?
Medium
- A2.5 m/s²
- B0.4 m/s²
- C160 m/s²
- D20 m/s²
26.A velocity-time graph shows a car accelerating from 0 m/s to 30 m/s over 10 seconds. What distance does the car travel during this time?
Hard
- A150 m
- B300 m
- C30 m
- D3 m
27.Which of the following can be found from a velocity-time graph? (Select all that apply)
Hard
- AThe acceleration from the gradient
- BThe distance travelled from the area under the graph
- CThe speed of the object at a given time
- DThe mass of the object
- EThe resultant force from the gradient
28.A car accelerates uniformly from rest at 2 m/s² over a distance of 25 m. What is its final speed?
Medium
- A10 m/s
- B50 m/s
- C100 m/s
- D5 m/s
29.A train travelling at 30 m/s applies its brakes and decelerates uniformly to rest over a distance of 450 m. What is the magnitude of its deceleration?
Hard
- A1 m/s²
- B2 m/s²
- C0.5 m/s²
- D15 m/s²
30.A student uses a single light gate to measure the speed of a toy car. Which measurements are needed?
Medium
- AThe length of the flag and the time the light gate is blocked
- BThe mass of the car and the time the light gate is blocked
- CThe distance between two light gates and the mass of the car
- DThe length of the flag and the mass of the car
31.Which piece of equipment is most suitable for measuring the length of an athletics track?
Medium
- AA trundle wheel
- BA metre rule
- CA stopwatch
- DA light gate
32.The typical walking speed of a person is about 1.5 m/s.
Easy
True or false?
33.The speed of sound in air is typically about 330 m/s.
Medium
True or false?
34.A driver's thinking distance depends on which of the following?
Medium
- AThe driver's reaction time and the car's speed
- BThe condition of the car's brakes and the road surface
- CThe mass of the car and the braking force
- DThe road surface and the tyre condition
35.Which of the following increase a car's braking distance? (Select all that apply)
Medium
- AWorn brake pads
- BAn icy road surface
- CA driver who has been drinking alcohol
- DA higher driving speed
- EWorn-out tyres
36.A car travels 60 km due north and then 60 km due south. Which of the following statements about the journey is correct?
Medium
- AThe distance travelled is 120 km and the displacement is 0 km
- BThe distance travelled is 0 km and the displacement is 120 km
- CThe distance travelled is 120 km and the displacement is 120 km north
- DThe distance travelled is 60 km and the displacement is 0 km
37.A cyclist rides at a constant speed of 5 m/s around a circular track. Which statement best describes the cyclist's motion?
Medium
- AThe speed is constant but the velocity is changing because the direction is changing
- BBoth the speed and the velocity are constant
- CThe velocity is constant but the speed is changing
- DBoth the speed and the velocity are changing
38.A car is moving along a straight road at a steady 15 m/s. Which of the following statements are correct? (Select all that apply)
Medium
- AThe car's speed is constant
- BThe car's velocity is constant
- CThe car is accelerating
- DThe resultant force on the car is zero
- EThe car's velocity is changing
39.A cyclist travelling at 12 m/s decelerates at 3 m/s². How long does it take the cyclist to stop?
Medium
- A4 s
- B3 s
- C9 s
- D36 s
40.A distance-time graph shows a straight line rising from 0 m to 90 m in 15 s. What is the object's speed?
Medium
- A6 m/s
- B15 m/s
- C90 m/s
- D1350 m/s
41.Florence Griffith Joyner set the women's 100 m world record in 10.49 s. Calculate her average speed during the race. Give your answer to 2 decimal places.
Medium
42.Complete the sentence using the correct words.
Easy
A straight, horizontal line on a distance-time graph means the object is ____. A steeper slope on a distance-time graph means the object is moving at a ____ speed.
43.Complete the sentence about acceleration.
Easy
Acceleration is defined as the rate of change of ____, and it is measured in ____.
44.A car accelerates uniformly from 5 m/s to 15 m/s over a distance of 50 m. Calculate its acceleration. Give your answer in m/s².
Medium
45.A runner completes a 100 m race in 12.5 s. Calculate the runner's average speed. Give your answer in m/s.
Medium
46.A driver has a reaction time of 0.6 s and is travelling at 15 m/s. Calculate the driver's reaction (thinking) distance. Give your answer in metres.
Medium
47.A driver is travelling at 20 m/s with a reaction time of 0.5 s. The braking distance at this speed is 24 m. Calculate the total stopping distance. Give your answer in metres.
Hard
48.Complete the equation for stopping distance.
Medium
stopping distance = ____ distance + ____ distance
49.Give the name of the distance a car travels while the driver is reacting before applying the brakes.
Medium
50.Driver B travels at 10 m/s with a reaction time of 0.6 s. Calculate the thinking distance for driver B. Give your answer in metres.
Medium
51.Driver B has a braking distance of 6 m at this speed. Calculate the stopping distance for driver B. Give your answer in metres.
Medium
52.Explain the difference between distance and displacement.
Hard
53.A car's speed increases from 20 m/s to 30 m/s. Explain why the braking distance increases. Use ideas about energy in your answer.
Hard
54.Florence Griffith Joyner set the women's 100 m world record in 10.49 s. Calculate her average speed during the race. Give your answer to 2 decimal places.
Medium
- A11.53 m/s
- B8.53 m/s
- C9.53 m/s
- D10.53 m/s
55.A car accelerates uniformly from 5 m/s to 15 m/s over a distance of 50 m. Calculate its acceleration. Give your answer in m/s².
Medium
- A1 m/s²
- B4 m/s²
- C2 m/s²
- D3 m/s²
56.A runner completes a 100 m race in 12.5 s. Calculate the runner's average speed. Give your answer in m/s.
Medium
- A10 m/s
- B7 m/s
- C8 m/s
- D9 m/s
57.A driver has a reaction time of 0.6 s and is travelling at 15 m/s. Calculate the driver's reaction (thinking) distance. Give your answer in metres.
Medium
- A11 m
- B9 m
- C10 m
- D8 m
58.A driver is travelling at 20 m/s with a reaction time of 0.5 s. The braking distance at this speed is 24 m. Calculate the total stopping distance. Give your answer in metres.
Hard
- A31 m
- B34 m
- C37 m
- D40 m
59.Driver B travels at 10 m/s with a reaction time of 0.6 s. Calculate the thinking distance for driver B. Give your answer in metres.
Medium
- A5 m
- B8 m
- C6 m
- D7 m
60.Driver B has a braking distance of 6 m at this speed. Calculate the stopping distance for driver B. Give your answer in metres.
Medium
- A12 m
- B11 m
- C13 m
- D14 m

Cartes mémo

What is the difference between distance and displacement?

Distance is how far an object moves and is a scalar quantity (no direction). Displacement is the distance moved in a straight line from start to finish, plus the direction, so it is a vector quantity.

Which of these are scalar quantities: distance, displacement, speed, velocity?

Distance and speed are scalars (magnitude only). Displacement and velocity are vectors (magnitude and direction).

What is the difference between speed and velocity?

Speed is how fast an object moves (scalar, no direction). Velocity is speed in a given direction, so it is a vector quantity.

Give typical speeds for a person walking, running and cycling.

Walking is about 1.5 m/s, running about 3 m/s and cycling about 6 m/s.

What is a typical value for the speed of sound in air?

About 330 m/s.

State the equation linking distance travelled, speed and time.

distance travelled = speed × time (s = v t), with s in metres, v in m/s and t in seconds.

How do you calculate the average speed of an object whose speed is changing?

average speed = total distance travelled ÷ total time taken.

On a distance–time graph, what does the gradient represent?

The gradient (change in distance ÷ change in time) equals the speed of the object.

What does a flat horizontal line on a distance–time graph show?

The object is stationary — it is not moving, so its distance from the start is not changing.

How can you find the speed of an accelerating object at a particular moment on a distance–time graph?

Draw a tangent to the curve at that time and calculate the gradient of the tangent.

Define acceleration and give its unit.

Acceleration is the rate of change of velocity. It is measured in metres per second squared (m/s²).

State the equation for average acceleration.

acceleration = change in velocity ÷ time taken (a = Δv / t), where Δv = final velocity − initial velocity.

How do you know from the sign of the acceleration that an object is slowing down?

If the acceleration is negative, the object is decelerating (slowing down).

What does the gradient of a velocity–time graph represent?

The gradient (change in velocity ÷ change in time) equals the acceleration of the object.

What does the area under a velocity–time graph represent?

The area under the graph represents the distance travelled (or displacement) by the object.

How do you find the distance travelled from a velocity–time graph?

Split the area under the line into triangles and rectangles, calculate each area, then add them together.

State the equation of motion that links final speed, initial speed, acceleration and distance.

v² − u² = 2 a s, where v is final speed, u is initial speed, a is acceleration and s is distance travelled.

What is the acceleration of a freely falling object near the Earth's surface (ignoring air resistance)?

About 9.8 m/s², often taken as 10 m/s². All objects fall with the same acceleration if there is no air resistance.

State Newton's First Law.

If the resultant force on an object is zero, a stationary object stays stationary and a moving object continues at the same speed in the same direction (constant velocity).

What happens to an object's velocity if a resultant force acts on it?

Its velocity changes — it speeds up, slows down, or changes direction. A resultant force is needed for any change in velocity.

Why does a vehicle travelling at a steady speed have a zero resultant force?

The driving force forwards is balanced by the resistive forces (such as friction and air resistance), so the resultant force is zero.

What is terminal velocity?

The constant velocity reached by a falling object when the upward forces (such as air resistance) balance the downward force of gravity, so the resultant force is zero.

Explain how a falling object reaches terminal velocity.

It initially accelerates due to gravity. As it speeds up, air resistance increases until it equals the weight, the resultant force becomes zero, and it falls at a constant terminal velocity.

What is stopping distance and how is it made up?

Stopping distance is the total distance a vehicle travels to stop. It is the sum of the thinking distance and the braking distance.

What is thinking distance and what affects it?

Thinking distance is the distance travelled while the driver reacts before braking. It depends on the driver's reaction time and the vehicle's speed.

What is braking distance and what affects it?

Braking distance is the distance travelled while the brakes are applied. It depends on the vehicle's speed and the braking force, and on road and tyre conditions such as wet or icy roads and worn tyres.

Why does braking distance increase as speed increases?

The brakes must remove more kinetic energy (kinetic energy = ½ m v²), and since kinetic energy depends on the square of the speed, doubling the speed roughly quadruples the braking distance.

Why does an intoxicated driver have a greater stopping distance?

Alcohol increases reaction time, so the thinking distance is longer and the total stopping distance is greater.

Why does a worn tyre increase braking distance?

Worn tyres give less grip (friction) between the tyres and the road, so the braking force is smaller and the car takes longer to stop.

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