- #1
iTheChosen1
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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
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.