Motion

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Lesson notes

Speed & Velocity

Speed = distance travelled per unit time; a scalar quantity (magnitude only).
Equation: v = \frac{s}{t} where v in m/s, s in m, t in s.
Average speed = total distance / total time; used when speed varies.
Velocity = speed in a given direction; a vector quantity.
Velocity uses displacement (vector) instead of distance.
Positive/negative signs indicate direction (e.g., +20 m/s east, −20 m/s west).

A hiker and a bee

Acceleration

Acceleration = rate of change of velocity; unit m/s².
Equation: a = \frac{\Delta v}{\Delta t} where \Delta v = v - u.
Positive acceleration = speeding up; negative acceleration = deceleration (slowing down).
Average acceleration useful when acceleration changes.

Positive and negative acceleration

Distance-Time Graphs

Gradient of a distance–time graph = speed.
Straight line = constant speed; horizontal line = stationary.
Steeper gradient = faster speed; curved line = changing speed (acceleration/deceleration).
To calculate speed: draw a large gradient triangle, find \frac{\Delta y}{\Delta x}.

Gradient of a distance-time graph

Speed-Time Graphs

Gradient of a speed–time graph = acceleration.
Straight line = constant acceleration; horizontal line = constant speed (zero acceleration).
Positive gradient = acceleration; negative gradient = deceleration.
Area under a speed–time graph = distance travelled.
Calculate area by splitting into triangles and rectangles: A = \frac{1}{2}bh (triangle) or A = bh (rectangle).

Area under a speed-time graph

Calculating Acceleration from Speed-Time Graphs

For constant acceleration: gradient = \frac{\Delta v}{\Delta t}.
For changing acceleration: draw a tangent at the point; gradient of tangent = instantaneous acceleration.
Use a large gradient triangle for accuracy.

Tangent to a speed-time graph curve

Freefall

In absence of air resistance, all objects fall with same acceleration of freefall g = 9.8\,\text{m/s}².
Velocity increases by 9.8 m/s each second.
Weight W = mg where g is also gravitational field strength (N/kg).

Freefall demonstration

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Practice questions

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1.Which of the following is a scalar quantity?
Easy
- Avelocity
- Bdisplacement
- Cspeed
- Dacceleration
2.Define speed.
Easy
3.A car travels 150 m in 10 s at constant speed. Calculate the speed.
Easy
- A17
- B15
- C16
- D14
4.Velocity is a vector quantity.
Easy
True or false?
5.Complete the sentence.
Easy
The gradient of a distance-time graph represents the ____ of the object.
6.Match each graph shape to the motion it represents.
Medium
- Horizontal line on distance-time graph
- Straight line with positive gradient on speed-time graph
- Curved line on speed-time graph with increasing gradient
- Stationary object
- Constant positive acceleration
- Increasing acceleration
7.Arrange the following speeds in order from slowest to fastest: 10 m/s, 5 m/s, 20 m/s, 15 m/s.
Easy
- 5 m/s
- 10 m/s
- 15 m/s
- 20 m/s
8.A train decelerates from 50 m/s to 42 m/s in 30 s. Calculate the deceleration (in m/s²).
Medium
- A-1.27
- B0.73
- C1.73
- D-0.27

More questions

9.What does the area under a speed-time graph represent?
Easy
10.A skydiver falls with constant acceleration of 9.8 m/s². After 5 s, what is their velocity (assuming they start from rest)?
Medium
- A9.8 m/s
- B49 m/s
- C98 m/s
- D2.0 m/s
11.From a speed-time graph, the area under the line between 0 s and 10 s is a triangle with base 10 s and height 20 m/s. Calculate the distance travelled.
Medium
- A90
- B120
- C100
- D110
12.Complete the sentence.
Easy
In the absence of air resistance, all objects fall with an acceleration of ____ m/s².
13.Speed is a vector quantity.
Easy
True or false?
14.Velocity is defined as speed in a given direction.
Easy
True or false?
15.Which of the following is a vector quantity?
Easy
- ADistance
- BSpeed
- CVelocity
- DTime
16.The gradient of a distance-time graph represents:
Easy
- AAcceleration
- BSpeed
- CDistance
- DTime
17.A horizontal line on a distance-time graph indicates the object is moving at constant speed.
Easy
True or false?
18.The area under a speed-time graph represents the distance travelled.
Easy
True or false?
19.An object accelerates from rest at 2 m/s² for 5 seconds. What is its final velocity?
Medium
- A2 m/s
- B5 m/s
- C10 m/s
- D25 m/s
20.A car decelerates from 20 m/s to 10 m/s in 4 seconds. What is the deceleration?
Medium
- A-2.5 m/s²
- B-10 m/s²
- C2.5 m/s²
- D10 m/s²
21.Match each term with its correct definition.
Medium
- Speed
- Velocity
- Acceleration
- Rate of change of velocity
- Distance per unit time
- Speed in a given direction
22.Arrange the following steps to calculate the acceleration from a speed-time graph:
Medium
- Draw a gradient triangle
- Calculate Δy/Δx
- Identify the section of graph
- Read the values of Δy and Δx
23.What is the definition of speed?
Easy
- ADistance travelled per unit time
- BChange in velocity per unit time
- CDistance travelled in a given direction per unit time
- DRate of change of displacement
24.Velocity is a scalar quantity.
Easy
True or false?
25.A person runs 5000 m in 1200 s and then walks a further 3000 m in 1800 s. What is their average speed for the whole journey?
Medium
- A1.7 m/s
- B2.7 m/s
- C2.9 m/s
- D5.8 m/s
26.The diagram shows a speed-time graph for a car journey. The graph consists of a straight line from (0,0) to (40,20), a horizontal line from (40,20) to (70,20), and a straight line from (70,20) to (90,0). What is the total distance travelled?
Medium
- A600 m
- B800 m
- C1000 m
- D1200 m
27.The acceleration of free fall near Earth's surface is approximately:
Easy
- A9.8 m/s
- B9.8 m/s²
- C9.8 m
- D9.8 km/h
28.The gradient of a distance-time graph represents acceleration.
Easy
True or false?
29.A speed-time graph shows a curve that is concave upwards (increasing gradient). Which statements about the object's motion are correct? (Select all that apply)
Hard
- AThe object is accelerating.
- BThe acceleration is constant.
- CThe speed is increasing at an increasing rate.
- DThe acceleration is increasing.
30.Match each section of a distance-time graph to the type of motion it represents.
Medium
- Horizontal line
- Straight line sloping upward
- Curve with increasing gradient
- Stationary
- Constant speed
- Accelerating
31.Arrange the following steps in the correct order to calculate the acceleration from a speed-time graph:
Medium
- Draw a large gradient triangle on the straight-line section.
- Determine the change in speed (Δv) and change in time (Δt).
- Calculate acceleration = Δv / Δt.
- Identify the section of the graph where acceleration is constant (straight line).
32.A student measures the time taken for a toy car to travel a fixed distance along a ramp. They repeat the measurement five times and obtain the following times: 2.1 s, 2.3 s, 2.0 s, 2.2 s, 2.1 s. What is the average time?
Easy
- A2.1 s
- B2.14 s
- C2.2 s
- D2.3 s
33.In an experiment to investigate the motion of a falling object, a student drops a ball from a height of 2.0 m and measures the time of fall. Which piece of equipment is most appropriate to measure the time accurately?
Medium
- AA stopwatch
- BA light gate connected to a data logger
- CA wristwatch with a second hand
- DA pendulum clock
34.A student records the distance travelled by a trolley rolling down a ramp at 0.5 s intervals. The results are shown in the table below. Which statement about the motion is correct? | Time interval (s) | Distance travelled (m) | |---|---| | 0.0–0.5 | 0.2 | | 0.5–1.0 | 0.6 | | 1.0–1.5 | 1.0 |
Medium
- AThe trolley is moving at constant speed.
- BThe trolley is accelerating.
- CThe trolley is decelerating.
- DThe trolley is stationary.
35.Which of the following are correct methods to determine the speed of a moving object in a school laboratory? (Select all that apply)
Medium
- AUsing a light gate and data logger to measure time over a known distance.
- BUsing a stopwatch to time the object over a measured distance.
- CUsing a ruler to measure the distance and a clock to measure time.
- DUsing a speedometer directly attached to the object.
36.Match each description of motion to the correct shape on a distance-time graph.
Medium
- Stationary
- Constant speed away from start
- Constant speed towards start
- Horizontal line
- Straight line with positive gradient
- Straight line with negative gradient
37.Arrange the following steps in the correct order to calculate the distance travelled from a speed-time graph.
Medium
- Identify the shapes under the graph (triangles, rectangles).
- Calculate the area of each shape.
- Sum the areas of all shapes.
- Draw the speed-time graph with labelled axes.
38.In an experiment to measure the acceleration of free fall, a student drops a ball from a height of 1.5 m and measures the time of fall as 0.55 s. What is the experimental value of g? (Use s = ½ g t²)
Medium
- A9.9 m/s²
- B9.8 m/s²
- C10.0 m/s²
- D9.5 m/s²
39.A car travels 150 m in 10 s at constant speed. What is its speed?
Easy
- A15 m/s
- B1.5 m/s
- C1500 m/s
- D0.067 m/s
40.Which of the following statements about the acceleration of free fall are correct? (Select all that apply)
Medium
- AIn the absence of air resistance, all objects fall with the same acceleration regardless of mass.
- BThe acceleration of free fall is approximately 9.8 m/s².
- CThe acceleration of free fall is greater for heavier objects.
- DThe acceleration of free fall is also called acceleration due to gravity.
41.The gradient of a distance-time graph represents the velocity of the object.
Easy
True or false?
42.Complete the sentence: The acceleration of free fall near Earth's surface is approximately ___ m/s².
Easy
The acceleration of free fall near Earth's surface is approximately ____ m/s².
43.State the equation that links average speed, distance, and time.
Easy
44.A car travels 150 m in 10 s at constant speed. Calculate the speed of the car.
Easy
45.A ball is dropped from rest and falls freely under gravity. Assuming no air resistance, calculate its velocity after 5 seconds. (Take g = 9.8 m/s²)
Easy
46.Complete the sentence:
Easy
Velocity is defined as speed in a given ____.
47.A car travels at a constant speed of 20 m/s. How far does it travel in 2 minutes? Give your answer in metres.
Easy
48.A stone is dropped from rest and falls freely under gravity. What is its velocity after 3 seconds? (Take g = 9.8 m/s²)
Easy
49.A cyclist accelerates from 5 m/s to 15 m/s in 4 seconds. Calculate the acceleration.
Easy
50.Explain how the distance travelled can be determined from a speed-time graph.
Medium
51.Describe an experiment to determine the acceleration of a trolley rolling down a ramp. Include the measurements you would take and how you would use them to calculate acceleration.
Hard
52.A ball is dropped from rest and falls freely under gravity. Assuming no air resistance, calculate its velocity after 5 seconds. (Take g = 9.8 m/s²)
Easy
- A59 m/s
- B44 m/s
- C54 m/s
- D49 m/s
53.A car travels at a constant speed of 20 m/s. How far does it travel in 2 minutes? Give your answer in metres.
Easy
- A2400 m
- B2640 m
- C2880 m
- D2160 m
54.A stone is dropped from rest and falls freely under gravity. What is its velocity after 3 seconds? (Take g = 9.8 m/s²)
Easy
- A32.3 m/s
- B35.2 m/s
- C26.5 m/s
- D29.4 m/s
55.A cyclist accelerates from 5 m/s to 15 m/s in 4 seconds. Calculate the acceleration.
Easy
- A1.5 m/s²
- B2.5 m/s²
- C3.5 m/s²
- D4.5 m/s²

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