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Car's momentum before the brakes were applied calculation
The car was driven at a constant speed. The driver applied the maximum braking force, and the braking distance was measured.
The test was repeated at different speeds. Figure 8 shows the results.
During one test the brakes were applied with a force of 6250 N.
The deceleration of the car was 5.0 m/s².
The braking distance of the car was 14.4 m.
Determine the momentum of the car before the brakes were applied.
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Marking points
- 1 Uses F = ma with the braking force and deceleration.
- 2 Rearranges to divide force by deceleration.
- 3 Finds the car's mass as 1250 kg.
- 4 Reads about 12 m/s (11.8–12.2 m/s accepted) from Figure 8 at 14.4 m.
- 5 Uses p = mv with the mass and graph-derived speed.
- 6 Obtains 15 000 kg m/s, with the official graph-read and error-carried-forward allowances.
Full-mark answer
From F = ma, m = F/a = 6250/5.0 = 1250 kg. Reading Figure 8 at a braking distance of 14.4 m gives a speed of about 12 m/s. Therefore p = mv = 1250 × 12 = 15 000 kg m/s.
Why this answer loses marks
I used the braking distance as the velocity in the momentum equation.
Distance and velocity are different quantities; the matching speed must be read from the graph first.