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Velocity-time graphs

Velocity-time graphs show how the velocity (or speed) of a moving object changes with time.

These graphs also show if the object is moving at a constant speed or accelerating, decelerating, or still.

What is shown on the velocity-time graph?

The area under the graph is the distance moved.

The gradient or the steepness of the graph can be used to work out the acceleration. A steep line means high acceleration.

A line upwards curving to become steeper means that the vehicle is accelerating at an increasing rate – non-uniform acceleration.

A line upwards curving to become flat means that the vehicle is accelerating at a decreasing rate to constant speed.

Remember, acceleration is the same as gradient, and acceleration = velocity change ÷ time.

Look at the graph. The acceleration of the vehicle in the first 10 seconds is:

= (40 m/s – 0 m/s) ÷ 10 s

= 4 m/s²

The acceleration of the vehicle between 20 and 30 seconds is:

= (60 m/s – 40 m/s) ÷ 10 s

= 2 m/s²

The acceleration of the vehicle between 30 and 50 seconds is:

= (0 m/s – 60 m/s) ÷ 20 s

= -3 m/s² (decelerating)

To find the distance travelled, look at the area under the graph.

In the first 10 seconds this is the area of the triangle, ½ × 10 s × 40 m/s = 200 m.

From 10 to 20 seconds this is the area of the rectangle, 10 s × 40 m/s = 400 m.

From 20 to 30 seconds this is the area of the rectangle and triangle, (10 s × 40 m/s) + (½ × 10 s × 20 m/s) = 500 m.

From 30 to 50 seconds, this is the area of the triangle, ½ × 20 s × 60 m/s = 600 m.

Total distance travelled = 200 m + 400 m + 500 m + 600 m = 1700 m.

Average speed = total distance ÷ total time = 1,700 m ÷ 50 s = 34 m/s.

Look at this velocity-time graph and answer the question. This question requires an extended response, ie your answer must be fairly long.