Lesson focus: Speed describes distance per time, velocitySpeed in a given direction; it is a vector, so a change of direction is a change of velocity. includes direction, and accelerationThe rate of change of velocity: acceleration = change in velocity ÷ time taken, measured in m/s². describes how velocity changes per time.
Use speed and acceleration equations with consistent SI units and interpret signs.
Build on earlier learning
SpeedYear 8 calculated average speed. This lesson adds velocity change and acceleration.
You will be successful when you can…
- Use v = s/t.
- Use a = (v − u)/t.
- Convert common units.
- Interpret negative acceleration.
Words that carry the science
- average speed
- Total distance travelled divided by total time.
- instantaneous speed
- Speed at a particular moment.
- velocity
- Rate of change of displacement in a stated direction.
- acceleration
- Change in velocity divided by time.
- deceleration
- Acceleration opposite to the current direction of motion, reducing speed.
- metre per second squared
- The SI unit m s⁻², meaning velocity changes by metres per second each second.
Average speed compresses a whole journey
01Average speed compresses a whole journey
Use average speed = total distance ÷ total time. It does not reveal stops or changing speed within the journey.
Convert kilometres to metres and hours to seconds before substituting when SI units are required. One m s⁻¹ equals 3.6 km h⁻¹.
02Acceleration measures velocity change
Use a = (v − u) ÷ t, where u is initial velocitySpeed in a given direction; it is a vector, so a change of direction is a change of velocity., v is final velocity and t is time. The unit m s⁻² means velocity changes by that many m s⁻¹ each second.
Signs depend on the chosen positive direction. Negative accelerationThe rate of change of velocity: acceleration = change in velocity ÷ time taken, measured in m/s². does not always mean slowing; an object moving in the negative direction can speed up with negative acceleration.
03Equations require a defined interval
Average acceleration over an interval can hide changing acceleration. State the interval and direction when interpreting results.
The speed equation uses distance, while average velocity uses displacement. Mixing them can produce a numerically plausible but conceptually wrong answer.
Acceleration down a ramp
Release a trolley at the top of a ramp. Two light gates measure its speed at two points. Acceleration is the change in speed divided by the time taken: a = (v − u) ÷ t. A steeper ramp gives a bigger acceleration; friction reduces it. The animation runs at just over half speed.
Controls
Friction values are illustrative; real trolleys and tracks vary. The gradient of the speed–time graph is the acceleration.
Calculate acceleration
A bicycle’s velocity increases from 4.0 m s⁻¹ east to 10.0 m s⁻¹ east in 3.0 s.
- Choose east as positive.
- Change in velocity = 10.0 − 4.0 = 6.0 m s⁻¹.
- a = 6.0 ÷ 3.0.
- a = 2.0 m s⁻² east.
How to make the reasoning visible: Velocity increases by 2.0 m s⁻¹ each second over the stated interval.
Audit motion calculations
Calculate or check each result using consistent units.
| Initial v / m s⁻¹ | Final v / m s⁻¹ | Time / s | Acceleration / m s⁻² |
|---|---|---|---|
| 0 | 12 | 4 | +3 |
| 15 | 5 | 5 | −2 |
| −2 | −8 | 3 | −2 |
| 8 | 8 | 6 | 0 |
Which row is speeding up despite negative acceleration?
What does zero acceleration in the last row mean?
Check your understanding
Answer from memory, then check against the suggested answer.
State the average-speed equation.
State the acceleration equation.
What does m s⁻² mean?
A car travels 18 km in 20 min. Calculate average speed in m s⁻¹.
Why can average velocity be zero when average speed is not?
Exam Question Practice
Exam Question Practice
Mark points shown after marking
A train slows from 25 m/s to 7 m/s in 12 s.
Calculate the acceleration of the train. Show your working.
(4)Explain what the sign of your answer shows.
(1)Total for this question: 5 marks
Command word: For calculateA command word: work out a number answer, showing your working and the unit., retain the sign and interpret it using your stated positive direction.