Calculating Acceleration from Speed-Time Graphs

Exam code: 5054

Written by: Ashika|Reviewed by: Caroline Carroll|Updated 2 July 2026

Interpreting Speed-Time graphs

An object may accelerate at a steady rate, this is called constant acceleration
- On a speed-time graph this will be a non-horizontal straight line

An object may accelerate at an increasing rate
- On a speed-time graph this would be an upward curve

An object may accelerate at a decreasing rate
- On a speed-time graph this would be an upward curve with a decreasing gradient

An object is said to decelerate if its speed is decreasing over time, i.e. its acceleration is negative
- On a speed-time graph this would be a downward line
  - If the line is a non-horizontal straight line, deceleration is constant
  - If the line is a curve with an increasing gradient, deceleration is increasing
  - If the line is a curve with a decreasing gradient, deceleration is decreasing

The acceleration of an object can be calculated from the gradient of a speed-time graph

$a c c e l e r a t i o n = g r a d i e n t = \frac{r i s e}{r u n}$

How to find the gradient of a speed-time graph

Worked example

Tora is training for a cycling tournament.

The speed-time graph below shows her motion as she cycles along a flat, straight road.

(a) In which section (A, B, C, D, or E) of the speed-time graph is Tora’s acceleration the largest?

(b) Calculate Tora’s acceleration between 5 and 10 seconds.

Part (a)

Step 1: Recall that the slope of a speed-time graph represents the magnitude of acceleration

The slope of a speed-time graph indicates the magnitude of acceleration
Therefore, the only sections of the graph where Tora is accelerating is section B and section D
Sections A, C, and E are flat – in other words, Tora is moving at a constant speed (i.e. not accelerating)

Step 2: Identify the section with the steepest slope

Section D of the graph has the steepest slope
Hence, the largest acceleration is shown in section D

Part (b)

Step 1: Recall that the gradient of a speed-time graph gives the acceleration

Calculating the gradient of a slope on a speed-time graph gives the acceleration for that time period

Step 2: Draw a large gradient triangle at the appropriate section of the graph

A gradient triangle is drawn for the time period between 5 and 10 seconds below:

Step 3: Calculate the size of the gradient and state this as the acceleration

acceleration = gradient = 5 ÷ 5 = 1 m/s²