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

Answer:

20 seconds

Step-by-step explanation:

Given:

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

The speed is the change in position.

So,

$Speed\ of\ car=\frac{ds}{dt} = \frac{d}{dt} (60t) -\frac{d}{dt} (1.5t^2)\\=60-2t(1.5)\\=60-3t$

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

$60-3t=0\\3t=60\\t = \frac{60}{3}\\ t=20$

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