Velocity-time graphs continued

Here is a velocity-time graph:

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.

The area under the line in a velocity-time graph represents the distance travelled. To find the distance travelled in the graph above, you need to find the area of the light-blue triangle and the dark-blue rectangle.

1. Area of light-blue triangle

The width of the triangle is 4 seconds and the height is 8 metres per second. To find the area, you use the equation:

area of triangle = ½ × base × height

So, the area of the light-blue triangle is ½ × 8 × 4 = 16 m

2. Area of dark-blue rectangle

The width of the rectangle is 6 seconds and the height is 8 metres per second. So, the area is 8 × 6 = 48 m

3. Area under the whole graph

The area of the light-blue triangle plus the area of the dark-blue rectangle is:

16 + 48 = 64 m

This is the total area under the distance-time graph. This area is the distance covered.