Run a 100 m race and watch both exam graphs draw themselves. The gradient of a distance–time graph is speed; the gradient of a velocity–time graph is acceleration. Drag along either graph to freeze any moment.
Model: a smooth velocity curve fitted to typical 10 m split times for each level of athlete. Times start from the athlete's first movement, so reaction time is not included. Velocity is positive towards the finish line. Not any individual athlete's data.
Teal dots mark where the sprinter was every 1 s: wider gaps = faster.
Worked example. A sprinter goes from 0 m/s to 9 m/s in 1.8 s. Acceleration = (9 − 0) ÷ 1.8 = 5 m/s². Always show the equation, the working and the unit.
| Shape of the line | On a distance–time graph | On a velocity–time graph |
|---|---|---|
| Horizontal (flat) | Stationary (not moving) | Constant velocity (zero acceleration). Flat on the time axis = stationary. |
| Straight, sloping up | Constant speed. Steeper = faster | Constant (uniform) acceleration |
| Curve getting steeper | Accelerating | Acceleration increasing |
| Curve getting flatter | Decelerating | Still accelerating, but by less and less |
| Sloping down | (Displacement–time only) moving back towards the start | Decelerating (negative acceleration), while velocity is positive |
Gradient = change in the y-axis ÷ change in the x-axis. On a distance–time graph that is metres ÷ seconds = speed. On a velocity–time graph it is (m/s) ÷ s = acceleration. On a curve, the gradient at one instant is the gradient of the tangent at that point, which is what the orange line in the lab shows.
Area under a velocity–time graph = displacement (and the area under a speed–time graph = distance). In the lab, the shaded area always matches the distance readout. You are far more likely to be asked to describe a graph than to calculate an area, but it shows why the two graphs belong together.
AQA questions often give split times and ask you to plot a graph. Here are a club sprinter's times at every 10 m. Set up the axes, plot each point, then compare your graph with the real curve.
Step 1: set up the axes. Which quantity goes on each axis?
Choose the axes first.
Step 3: interpret it. What does the shape of the curve show?
Quick sort. Scalar or vector?
Compare athletes in the lab: the elite athlete reaches a higher maximum velocity, holds it for longer and slows down the least. A less trained athlete reaches maximum velocity earlier and decelerates more.
Explain the difference between a scalar and a vector quantity. Give one example of each from linear motion.
A sprinter accelerates from 0 m/s to 8.4 m/s in the first 1.4 s of a race. Calculate the sprinter's average acceleration. Show your working.
A 400 m runner completes one lap and finishes on the start line in 50 s. Calculate the runner's distance, displacement, average speed and average velocity.
The velocity–time graph shows a footballer's movement. Describe the motion in sections A, B and C.
A sprinter's split times are: 10 m 2.0 s, 20 m 3.1 s, 30 m 4.2 s, 40 m 5.2 s, 50 m 6.2 s. Plot a distance–time graph and use it to describe the sprinter's motion.
Sketch and explain a velocity–time graph for an elite sprinter running a 100 m race.