Liam\'s daughter was taken again. He is in a car chasing after the bad guys who

Question

Liam's daughter was taken again. He is in a car chasing after the bad guys who are in a train. He is driving at a constant velocity v(t)=V-constant. When the car is L meters away the train begins to pull away with a constant acceleration a(t)=A-constant.

A) assuming Liam can catch the train, what time will he catch it?

B) How far has the train traveled from it's starting point in this time?

C) What is the minimum value of V constant must the car have to catch the train?

D) Sketch a position vs. time graph of the train and car.

Explanation / Answer

xliam = V t

x train = L + 1/2 a t^2

V t = L + 1/2 A t^2

t = ( V - sqrt( V^2 - 2 A L))/A

b)

dx train = 1/2 A t^2 = 1/2 A ( V - sqrt(V^2 - 2 A L))^2/A^2

= ( V - sqrt(V^2 - 2 A L))^2/( 2 A)

c) min time when V^2 - 2 A L = 0

v = sqrt( 2 A L)

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