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You should be able to calculate gradients of velocity-time graphs and the areas under the graphs.

The gradient of a line on a velocity-time graph represents the acceleration of the object. Study this velocity-time graph.

- Question
What is the acceleration represented by the sloping line?

- Answer
- The object increases its velocity from 0m/s to 8m/s in 4s.
- Its acceleration is 8 ÷ 4 = 2m/s
^{2}.

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

- 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 =
^{1}⁄_{2}× base × height - so the area of the light-blue triangle is
^{1}⁄_{2}× 8 × 4 = 16m.

- 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 = 48m.

- Area under the whole graph
- The area of the light-blue triangle plus the area of the dark-blue rectangle is:
- 16 + 48 = 64m.
- This is the total area under the distance-time graph. This area represents the distance covered.

- the gradient of a velocity-time graph represents the acceleration
- the area under a velocity-time graph represents the distance covered

Watch this illustrated podcast for a summary of distance/time and velocity/time graphs.

Check your understanding of this by having a go at the following activity.

Now try a Test Bite - higher

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