To avoid a collision what is your reaction time?

[KaseyK]

Homework Statement

As you are driving with a velocity of 75 km/h [N], you suddenly realize that there is a stalled vehicle in your lane 48.0m directly ahead. You react, applying the brakes to provide an acceleration of 4.80 m/s^2 . If you managed to avoid a collision what was your reaction time.

Homework Equations

What was your reaction time?

The Attempt at a Solution

First I wanted to find Vfinal so I used the kinematic equation Vf^2 = Vi^2 +2ad

I used:
Vi = 20.8333 m/s
d = 48.0 m
a = 4.80 m/s^2

This gave me Vf^2 = 29.9136 m/s

Then to find the time I used Vf = Vi + at

I got -1.89 s. The answer should be 0.13 s.

What did I do wrong?

 

[RoyalCat]

You applied the acceleration wrong.
You were looking to avoid the collision, did you accelerate towards the car, or did you want to stop (Vf=0) so as to avoid the collision?

 

[KaseyK]

I wanted to avoid the car so the acceleration should have been negative?

 

[BAnders1]

You want to know what distance the car travels before reaching a complete stop (where your final velocity is zero).

Consider the case in which your reaction time is instantaneous, and you hit the brakes when you are 48.0m away from the car. How close are you to the car before you stop? This distance is the same as the distance you could have waited before hitting the brakes.