A fugitive tries to hop on a freight train traveling at a constant speed of 4.5 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 3.4 m/s2 to his maximum speed of 8.0 m/s.
(a) How long does it take him to catch up to the empty box car?
s
(b) What is the distance traveled to reach the box car?

Question

A fugitive tries to hop on a freight train traveling at a constant speed of 4.5 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 3.4 m/s2 to his maximum speed of 8.0 m/s. 
(a) How long does it take him to catch up to the empty box car?
s
(b) What is the distance traveled to reach the box car?

anonymous · Answer

The answer is 15 seconds.

mani_jha · Answer

Let us assume that the fugitive catches the box after T seconds. If the fugitive catches up with it, the distance travelled by the train in time T and the fugitive in time T should be equal.
Distance travelled by train=4.5T
Time taken by fugitive to reach his maximum velocity = t = (v/a)=(8/3.4). After that, the fugitive travels with uniform velocity of 8 m/s.
Distance travellled by fugitive=$$at ^{2}/2 + 8(T-t)$$
Thus 4.5T=$$at ^{2}/2 + 8(T-t)$$. we know a, t. Find T.
Distance travelled to reach the car = $$at ^{2}/2 + 8(T-t)$$
As far as i think, this is correct. The answer doesnt matter