Calculate Your Reaction Time to Avoid a Car Accident - Homework Problem

[iTheChosen1]

Homework Statement

Reaction time can be crucial in avoiding a car accident. You are driving at 75 km/h [N] when you notice a stalled vehicle 48.0m directly ahead of you. You apply the brakes, coming to a stop just in time to avoid a collision. Your brakes provided a constant acceleration of 4.8m/s^2 . What was your reaction time.

Given:
Vi = 75 km/h [N] --> 20.8 m/s
d = 48 m
a = -4.8 m/s^2 [N]
Vf = 0

Homework Equations

d = vi.t + 1.2.a.t^2

The Attempt at a Solution

I tried using the quadratic formula by plugging in the neccesary numbers into
d = Vi.t + 1/2.a.t^2.

I plug in all the numbers and this is it

48 = 20.8.t - 2.4t^2

- 2.4t^2 + 20.8.t - 48 = 0

a = -2.4
b = 20.8
c = -48

Now just by calculating the discriminant, it turns out to be a negative value.

b^2 - 4ac = 20.8^2 - 4(-2.4 x -48)
= 432.64 - 460.8
=28.16

The answer is that the reaction took 0.13 s.

I assumed that there were going to be 2 roots, the one being positive would be the right answer.

 

[PhanthomJay]

Wecome to PF!

There is no acceleration during the reaction time (the vehicle moves at constant speed). The acceleration of -4.8 m/s^2 starts at a distance less than 48 m from the stalled car. You can determine this distance from one of the other kinematic equations, then continue from there to answer the question.

 

[Mike Pemulis]

Your method is slightly wrong. We can start by noting what the problem means by "reaction time." It's the time that passes between the driver noticing the stalled vehicle, and the driver hitting the brake. His car travels some distance during that time.

After he hits the brake, the car accelerates while traveling the rest of the distance, and comes to a stop just before hitting the stalled vehicle.

Knowing this, plus the distance, initial speed, and acceleration, we can find the reaction time -- the time before there is any acceleration.

Hopefully that makes it clearer.