Openstax: Section 4.10 Antiderivatives (problem number 509)

Question

A car is being driven at a rate of 40 mph when the brakes are applied. The car decelerates at a constant rate of 10 ft/sec2. How long before the car stops?

Answer 1

Deceleration is also known as negative acceleration.

a = -10

dv/dt = -10

∫dv = -10 ∫dt

v = -10t + C

Given that v = 40 mph in the beginning (t=0)

40 = -10(0) + C

C = 40

Therefore our function v in terms of t is:

v = -10t + 40

If the car stops, it means v = 0

0 = -10t + 40

10t = 40

t = 4 seconds

It means the car will stop in 4 seconds from the time the driver hit the break.