Mathematics for IGCSE & O level - Proportion (Section 3 - No. 24)
The braking distance, *d*, of a car is directly proportional to the square of its speed, *v*. If the braking distance is 6m when the speed is *v* meters per second, select the correct statements:
The expression for the speed of the car is d=kv^2.
If the speed is increased by 100%, the braking distance increases by 300%.
The braking distance is inversely proportional to the square of the speed.
The percentage increase in the braking distance is 300%
Explanation
The braking distance d = kv^2. If the speed v increased by 100%, it doubles. Thus if v' = 2v, d' = k(2v)^2 = 4kv^2. If d = 6 when the speed is v, then d'=4*6=24. Thus the braking distance increases by 300%.
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