# 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.

The table shows what each section of the graph represents:

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

## 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, whose motion is represented by the velocity-time graph below.

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

Find the area of the triangle:

Find the area of the rectangle:

base × height

(10 - 4) × 8 = 48 m2

Add the areas together to find the total displacement:

(16 + 48) = 64 m