Motion: revision notes and practice

What you will learn

• Distinguish distance, displacement, speed, velocity and acceleration.
• Calculate average speed and acceleration with consistent units and direction signs.
• Interpret motion graphs and relate measurements to road safety.

Key rules

Average speed

Average speed = total distance ÷ total time. Use metres and seconds for an answer in m/s.

Acceleration

a = (v − u)/t, where u is initial velocity and v is final velocity. Use velocities in m/s and time in s to get m/s².

Distance at constant speed

Distance = speed × time when speed is constant. Convert km to m by multiplying by 1000, and minutes to seconds by multiplying by 60.

Worked examples

Example 1: An object travels 1.8 km in 3 minutes. Find its average speed in m/s.

1. Convert distance: 1.8 × 1000 = 1800 m.
2. Convert time: 3 × 60 = 180 s.
3. Average speed = 1800 ÷ 180 = 10 m/s.

10 m/s

Example 2: Velocity changes from 20 m/s to 8 m/s in 4 s along the same straight line. Find acceleration.

1. Change in velocity = 8 − 20 = −12 m/s.
2. a = −12 ÷ 4 = −3 m/s².
3. The negative sign means acceleration is opposite the positive direction.

−3 m/s²

A practice question

An object travels 66.5 m in 7 seconds. Calculate its average speed in m/s.

1. Distance and displacement tell different stories

Distance is the total length of a route, with no direction attached. Displacement describes the change from the starting position to the final position and includes direction. Walking 3 m east then 3 m west gives a distance of 6 m but zero displacement. Both use metres; a shared unit does not make quantities identical.

Speed describes how fast distance is covered. Velocity includes direction. Two cars at 10 m/s travelling in opposite directions have equal speeds but different velocities. Choose a positive direction before working with signed velocities along one straight line.

2. Average speed uses the whole journey

Average speed is total distance divided by total time. Include waiting time when the question describes the entire journey. A cyclist covering 900 m in 180 s has average speed 5 m/s, even if the speed varied throughout the ride.

Rearrange to distance = average speed × time or time = distance/average speed. Do not simply average two speeds unless equal time was spent at each. Travelling 100 m at 5 m/s and another 100 m at 10 m/s takes 20 + 10 = 30 s, giving 200/30 ≈ 6.67 m/s.

Average speed = total distance ÷ total time

3. Make metres and seconds agree

For m/s, convert kilometres to metres and minutes to seconds before dividing. A 1.2 km journey in 4 minutes is 1200/240 = 5 m/s. For km/h to m/s, divide by 3.6 because one kilometre is 1000 m and one hour is 3600 s.

Thus 72 km/h is 20 m/s. To reverse the conversion, multiply by 3.6. Write the converted values next to their units so you can spot mistakes. The letter s can represent distance in an equation, while s written after a number denotes the unit second.

4. Acceleration measures a change in velocity

Use a = (v − u)/t, with initial velocity u and final velocity v. An increase from 4 to 16 m/s in 6 s gives 2 m/s². Each second, velocity increases by 2 m/s if acceleration stays constant. Rearranging gives v = u + at.

Keep signs consistent. Changing from +12 to +4 m/s in 2 s gives −4 m/s²: acceleration is opposite the positive direction. Negative acceleration does not always mean slowing down. An object going from −4 to −8 m/s speeds up in the negative direction while its acceleration is negative.

a = (v − u)/t; a in m/s², velocities in m/s, t in s

5. Read distance–time graphs by their gradient

On a distance–time graph for motion along a line, gradient gives speed: change in distance divided by change in time. A line rising 30 m over 6 s represents 5 m/s. A steeper line means a larger speed; a horizontal line means the plotted distance is unchanged, so the object is stationary.

A changing gradient indicates changing speed. Read both axes and their units before calculating. Higher extension for AQA: draw a tangent to a curved distance–time graph to estimate speed at one instant. Use two well-separated points on that tangent, rather than dividing coordinates from the curve.

6. Velocity–time graphs have another meaning

A velocity–time graph's gradient gives acceleration, not speed. A horizontal line means constant velocity, which may be zero or non-zero. A line from 0 to 12 m/s over 4 s has acceleration 3 m/s². A downward gradient means negative acceleration in the chosen coordinate direction.

Higher extension for AQA: signed area between the graph and time axis gives displacement. For the example's triangular area, displacement is ½ × 4 × 12 = 24 m. Areas below the axis are negative for displacement; add their magnitudes instead when finding total distance.

7. Use assumptions instead of forcing an equation

When acceleration is constant along a straight line, v² − u² = 2as links velocities, acceleration and distance without time. From rest, accelerating at 2 m/s² over 9 m gives v² = 36 and speed 6 m/s. Keep the quantities and direction convention consistent; take care when interpreting a square-root result.

Freely falling objects near Earth accelerate at about 9.8 m/s² if air resistance is negligible. A falling object in air may reach terminal velocity as resistance grows to balance weight. Higher extension for AQA: constant speed around a circle still means changing velocity because the direction changes.

v² − u² = 2as, for constant acceleration

8. Measure motion and explain stopping distance

Measure a known distance and travel time to estimate average speed. Light gates can reduce reaction-time uncertainty compared with a hand stopwatch. For acceleration, measure velocities at different times rather than dividing distance by time twice. Repeat trials and control the track angle and release method; do not give the trolley an extra push.

Stopping distance = thinking distance + braking distance. Thinking distance depends on speed and reaction time; tiredness or distraction can increase it. Braking depends on factors including speed, grip and brake condition. Doubling speed doubles thinking distance for unchanged reaction time, while braking distance typically grows more strongly under comparable conditions.

Check your understanding

How to earn the marks

• Do not confuse distance/time with change in velocity/time; their units differ.
• Write your positive direction and preserve negative signs until interpretation.
• On a graph, identify the axes before choosing gradient or area.
• Use the full journey's time for average speed, including stops when relevant.

A common mistake

Do not mix km with seconds if the answer needs m/s. Negative acceleration does not always mean slowing down; consider the velocity direction.

Course context and official specifications

This guide covers selected skills. Some extensions are Higher content; choose your official tier separately from practice difficulty in the app. These are original questions and explanations.

• AQA GCSE Physics — 4.5.6.1

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• Edexcel GCSE Physics — 2.5–2.8

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Gateway GCSE Physics A — P2.1; PM2.1

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

• OCR Twenty First Century GCSE Physics B — P4.2

  The core calculations in this bank are selected separate Physics skills. Foundation and Higher content differ within these larger sections; this is not complete topic coverage.

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