# Velocity-time graphs

### Determining acceleration

If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the of the object.

A velocity-time graph

The table shows what each section of the graph represents:

APositiveIncreasingPositive
BZeroConstantZero
CNegativeDecreasingNegative
D (v = 0)ZeroStationary (at rest)Zero
Question

Calculate the acceleration of the object represented by the steepest line in the graph.

change in velocity = (10 − 0) = 10 m/s

change in time = (2 − 0) = 2 s acceleration = 10 ÷ 2 ### Calculating displacement - Higher

The of an object can be calculated from the area under a velocity-time graph. The area under the graph can be calculated by:
• using geometry (if the lines are straight)
• counting the squares beneath the line (particularly if the lines are curved)

### Example

Calculate the total displacement of the object - its motion is represented by the velocity-time graph below.

The y-axis shows velocity in metres per second and the x-axis time in seconds. The object increases its velocity from 0 metres per second to 8 metres per second in 4 seconds

Here, the displacement can be found by calculating the total area of the shaded sections below the line.

1. Find the area of the triangle:
• • 2. Find the area of the rectangle:
• • 3. Add the areas together to find the total displacement: 