If a car is travelling at 100km/h and takes 68m to stop at a constant acceleration, how long does it take to stop?

These notes accompany the video Braking distance.

Imagine that a car is travelling on a straight road. The driver sees a problem on the road

ahead and so brakes suddenly to stop. The stopping distance is the distance that the car

travels from the moment that the brakes are applied to the moment that the car stops.

This is also called the braking distance.

If the car is initially travelling at u m/s, then the stopping distance d m travelled by the

car is given by

d =

u

2

20

.

We will see later in these notes how this formula is obtained.

This formula means that the stopping distance is directly proportional to the square of

the speed of the car at the instant the brakes are applied. That is,

d ∝ u

2

.

We refer the reader to the TIMES module Proportion (Years 9–10). So in general, the

stopping distance d from initial speed u is given by a formula of the form

d = ku2

,

where the constant of proportionality k depends on the units being used.

What happens if the initial speed of the car is increased by 10%?

This doesn’t seem much — for example, increasing your speed from 50 km/h to 55 km/h

is a 10% increase. To see the effect, we take u = 1 and so d = k. A 10% increase gives

u = 1.1, and so

d = (1.1)2

k = 1.21k.

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