Question

A driver who is moving at 15 m/s, sees a stop light and puts on the brakes 30 m before an intersection.

a) What acceleration will the driver have to have to stop before entering the intersection?

b) How much time will it take to stop the car?

Answer 1

Hi there!

We can use the kinematic equation:

`vf^2 = vi^2 + 2ad`

vf = final velocity (0 m/s)

vi = initial velocity (15 m/s)

a = acceleration due to breaking (? m/s²)

d = displacement (30 m)

We can plug in the given values:

`0^2 = 15^2 + 2(a)(30)\\\\0 = 225 + 60a`

Solve:

`-60a = 225 \\\\a = \boxed{-3.75 m/s^2}`

To solve for the time taken, we can use the following:

`t= (v_f-v_i)/(a)`

Plug in the values:

`t = (0-15)/(-3.75) = \boxed{4 sec}`