FRICTION AND BRAKING
3 marks · HardThe table below gives the thinking distance and braking distance for a car at two different speeds in ideal conditions.
| Speed (mph) | Thinking distance (m) | Braking distance (m) |
|---|---|---|
| 30 | 9 | 14 |
| 60 | 18 | 55 |
Compare how thinking distance and braking distance change when the speed doubles from 30 mph to 60 mph.
Explain why braking distance increases much more than thinking distance as speed increases.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) When speed doubles, the thinking distance also doubles (9 m to 18 m), but the braking distance increases by a much greater factor (from 14 m to 55 m, about 4 times larger). · must show thinking distance doubles, braking distance increases by about 4 times
(b) Braking distance increases more because the car's kinetic energy depends on speed squared, so more energy must be removed to stop at higher speeds. · must show braking distance increases with speed squared or kinetic energy point
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · States or shows that thinking distance doubles (9 to 18 m)
B2 (a) · 1 mark · States or shows that braking distance increases by more than double or by about 4 times (14 m to 55 m)
B3 (b) · 1 mark · Explains that braking distance increases with the square of speed/kinetic energy
Worked solution
a) As speed doubles from 30 mph to 60 mph:
- Thinking distance doubles from 9 m to 18 m.
- Braking distance increases from 14 m to 55 m (almost four times larger).
b) Braking distance increases more quickly because kinetic energy is proportional to speed squared; more energy must be removed to stop at higher speed.