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Learn0625Papers 1, 3 · CoreMotion, forces and energySpeed, velocity and acceleration
Motion, forces and energy · Subtopic 2 of 10

Speed, Velocity and Acceleration

Speed is distance per unit time; velocity is speed in a given direction. Acceleration is the rate of change of velocity. On a distance–time graph the gradient is speed; on a speed–time graph the gradient is acceleration and the area underneath is the distance travelled.

Cambridge 5054 Paper 1Cambridge 5054 Paper 2Cambridge 0625 Papers 2, 4Cambridge 0625 Papers 1, 3Edexcel 4PH1 Paper 1PEdexcel 4PH1 Paper 2P≈ 35 minRevision 6 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Calculate speed and average speed, converting units where needed.
  • Interpret distance–time graphs: the gradient is speed.
  • Calculate acceleration and deceleration.
  • Use speed–time graphs: the gradient is acceleration, the area is distance.
Pause and think

A car's speedometer reads a steady 5050 km/h as it drives round a roundabout. Is its velocity constant?

Section 2 of 14

Core idea

Start hereA skydiver who stops speeding up

Jump from a plane and you speed up, but not forever: after about 12 seconds you fall at a steady 55 m/s. Something is pushing back harder the faster you go. Describing motion starts with speed and acceleration, and graphs that show both.

The big idea

Speed =distancetime=\frac{\text{distance}}{\text{time}}; acceleration =change in velocitytime=\frac{\text{change in velocity}}{\text{time}}. Speed–time graph: gradient = acceleration, area = distance.

1. Speed and acceleration

v=sta=v−utv=\frac st\qquad a=\frac{v-u}t
where
ss
distance (m).
u,vu,v
initial, final velocity (m/s).
aa
acceleration (m/s²).
Worked exampleCar from rest

0 to 20 m/s in 8 s.

Goal
Acceleration and distance.
Strategy
Formula; area of the triangle under the graph.
  1. a=20−08=2.5 m/s2a=\frac{20-0}8=2.5\text{ m/s}^2
    Change in velocity ÷ time.
  2. s=12×8×20=80 ms=\tfrac12\times8\times20=80\text{ m}
    Triangle area.
Answer2.52.5 m/s²; 8080 m.
✓ CheckAverage speed 1010 m/s × 8 s = 80 m ✓.

2. Graphs

Speed–time graph of a car journey
102030405101520250time (s)speed (m/s)distance so farspeeding up: 2 m/s²steady 20 m/sbraking
Total distance == area =12(10)(20)+20(20)+12(10)(20)=600=\tfrac12(10)(20)+20(20)+\tfrac12(10)(20)=600 m.
Why area = distance
  1. s=v×t (constant speed)s=v\times t\ \text{(constant speed)}
    A rectangle under a flat line: height × width.
  2. s=∑v Δts=\sum v\,\Delta t
    Varying speed: split into thin strips, each nearly a rectangle.
Total distance = total area under the speed–time graph.
Worked exampleWhole journey

0 → 20 m/s in 8 s; 20 m/s for 30 s; stops in 10 s.

Goal
Distance and average speed.
Strategy
Add the areas.
  1. 80+20×30+12(10)(20)80+20\times30+\tfrac12(10)(20)
    Triangle + rectangle + triangle.
  2. =80+600+100=780 m=80+600+100=780\text{ m}
    Add.
  3. vˉ=780÷48=16.25 m/s\bar v=780\div48=16.25\text{ m/s}
    Total distance ÷ total time.
Answer780780 m; 16.2516.25 m/s.
✓ CheckBelow the top speed 20 m/s ✓.
Common misconceptionAverage of speeds Average speed is total distance ÷ total time, not the average of the speeds.

3. Falling and terminal velocity

An object falling with air resistance reaches terminal velocity
51015201020304050600time (s)speed (m/s)skydiverterminal velocity
At first it accelerates at g≈10g\approx10 m/s² (steep slope). Air resistance grows with speed until it equals the weight; then the acceleration is zero and the speed stays constant.
Reaching terminal velocity

Opening a parachute raises air resistance; the loop repeats to a lower terminal velocity.

Pause and think

Without air, how fast is a stone falling after 3 s?

Summary

  • Gradients and areas carry meaning.
  • Terminal velocity: forces balance.
Key words
Acceleration
Rate of change of velocity.
Terminal velocity
Constant top speed when forces balance.
HistoryGalileo's ramps. Around 16041604 Galileo rolled balls down gentle ramps, timing them with a water clock, and found the distance grew with the square of the time: steady acceleration. Slowing the fall with a ramp let him measure what was too quick to time directly.
Fun factFaster than a Formula 1 car. A cheetah reaches about 2525 m/s from rest in 33 s: an acceleration of about 88 m/s². That's close to a Formula 1 car's launch and almost the acceleration of free fall.
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