AQA · GCSE · Combined Science · Higher

Graph gradient and changing resultant force

Q06.3 3 marks

Figure 10 shows how the velocity of a car changes during braking.

Line graph titled Figure 10. The y-axis is velocity in metres per second from 0 to 30. The x-axis is time in seconds from 0 to 6. A curved line starts at 30 m/s at 0 s, decreases steeply at first, then more gradually, reaching 0 m/s at about 5 s and staying at zero to 6 s. — Figure 10

Explain how the gradient of the line on Figure 10 shows that the resultant force on the car was not constant.

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Marking points

1 State that the gradient of a velocity-time graph is the acceleration.
2 Use the curved graph to say that the gradient, and therefore the acceleration, is not constant.
3 Link this to resultant force using $F=ma$ : for a constant mass, a changing acceleration means a changing resultant force.

Full-mark answer

The gradient of a velocity-time graph is the acceleration. The line in Figure 10 is curved, so its gradient and the car’s acceleration are not constant. Since $F=ma$ , and the car’s mass is constant, a non-constant acceleration means the resultant force is not constant.

Why this answer loses marks

The velocity is decreasing so the force is not constant.

A decreasing velocity does not by itself show that the force is not constant; the key evidence is the changing gradient, which means changing acceleration.

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