Reading Speed-Time Graphs

A speed-time graph shows how the speed of an object changes over time. The gradient gives acceleration, and the area under the graph gives distance.

What do the features mean?

Feature	Meaning
Horizontal line	Constant speed (zero acceleration)
Straight line sloping upward	Constant (uniform) acceleration
Straight line sloping downward	Constant deceleration
Curved line	Non-uniform (changing) acceleration
Line at zero	Object is stationary

How do you calculate acceleration from the graph?

$\text{acceleration} = \text{gradient} = \frac{\Delta v}{\Delta t}$

Choose two points on a straight section, find the change in speed and divide by the change in time.

Worked example

A speed-time graph shows a car’s speed increasing from 0 m/s to 20 m/s in 10 s. Calculate the acceleration. [2]

$a = \frac{20 - 0}{10 - 0} = \frac{20}{10} = 2.0\ \text{m/s}^2$

Marking points: M1 for gradient calculation using two correct values. A1 for 2.0 m/s².

These marking points are for this original example and are not an official Cambridge mark scheme.

What does a negative gradient mean?

A downward slope means the speed is decreasing, so the acceleration is negative. The object is decelerating. If the line reaches zero on the speed axis, the object has stopped.

Common errors and how to correct them

• Confusing the gradient with the area. The gradient of a speed-time graph gives acceleration. The area under the graph gives distance. These are different quantities with different units.
• Reading the speed at one point instead of calculating the change. Acceleration requires the change in speed between two points, not the speed at a single time.
• Ignoring units on the axes. Always check the axis labels and scales before reading values. Speed might be in km/h, not m/s.

How to apply this in an exam

Draw a clear gradient triangle and label the sides with their values. This makes the calculation visible and earnable. For curved sections, draw a tangent at the required time and calculate the gradient of the tangent.