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Representing motion

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# Velocity-time graphs - higher

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.

Velocity - time graph

Question

What is the acceleration represented by the sloping line?

• The object increases its velocity from 0m/s to 8m/s in 4s.
• Its acceleration is 8 ÷ 4 = 2m/s2.

## The area

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.

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 = 12 × base × height
• so the area of the light-blue triangle is 12 × 8 × 4 = 16m.
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 = 48m.
3. 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.

## Summary

• 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.

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