Hello all. You are following another car on the highway at a distance of 37 m. Y

Question

Hello all.

You are following another car on the highway at a distance of 37 m. You are both driving at 25.48 m/s. Suddenly the car in front of you starts to break at a constant acceleration of 7 m/s2. Because you are distracted, you don't notice and proceed at constant velocity.
a) How much furthur do you travel, before crashing into the car in front of you?
b) What is the speed of the other vehicle?

Answers:
a) 82.9 m
b) 2.7 m/s

Please explain with an unconvoluted, straightforward way of solving. Thank you

Explanation / Answer

Part A)

The distance travelled by the braking car is...

d = vot + .5at2

d = (25.48)t + .5(-7)(t2)

d = 25.48t - 3.5t2

The distance traveled by the constant velocity car is

d + 37 = vt

d + 37 = 25.48t

d = 25.48t - 37

Set the d's equal...

25.48t - 37 = 25.48t - 3.5t2

That leaves 3.5t2 = 37

t = 3.25 sec

Then your distance travelled = vt

d = (25.48)(3.25)

d = 82.8 m/s

Part B)

The speed of the first car...

vf = vo + at

vf = 25.48 - 7(3.25)

vf = 2.73 m/s

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