Question

The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t − 1.5t2, t seconds after the driver applies the brakes. How many seconds after the driver applies the brakes does the car come to a stop?

Answer 1

20 seconds

Explanation:

Given:

Position of car = s(t) = 60t-1.5t^2

The speed is the change in position.

So,

`Speed\ of\ car=(ds)/(dt) = (d)/(dt) (60t) -(d)/(dt) (1.5t^2)\\=60-2t(1.5)\\=60-3t`

When the car will stop, the speed will be zero.

`60-3t=0\\3t=60\\t = (60)/(3)\\ t=20`

Therefore, the car will stop after 20 seconds of applying the break ..