Question

A car is moving at constant velocity +48.8 m/s along a straight highway. Suddenly the driver spots a stalled vehicle 378.7 m ahead, and steps on the brake. Find the acceleration needed, in m/s2, to just stop the car before running into the stalled car. The sign of your answer will give the direction of the acceleration.

Answer 1

Answer:

a = - 3.14[m/s^2]

Explanation:

To solve this problem we must use the following kinematic equation:

$v_{f} ^{2}= v_{o} ^{2}+2*a*dx\\where:\\v_{f} = final velocity = 0 [m/s]\\v_{o}= initial velocity = 48.8 [m/s]\\ a = acceleration [m/s^2]\\dx = displacement [m]$

Now replacing:

$0 = 48.8^{2}+2*a*(378.7) \\-2381.44 = 757.4*a\\a = -3.14[m/s^2]$

The negative sign means the vehicle slows down.