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

a = - 3.14[m/s^2]

Step-by-step 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.