(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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.

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# Reaction time problem

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