Question

A fugitive tries to hop on a freight train traveling at a constant speed of 5.2 m/s . Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 1.4 m/s2 to his maximum speed of 5.9 m/s .
So,How long does it take him to catch up to the empty box car?

Answer 1

How long does it take him to get to max speed? After that, how long does it take to catch up?
5.9/1.4 = 4.214 seconds to max out
So he will catch up after t seconds, where
5.2t = 1/2 * 1.4 * 4.214^2 + 5.9(t-1.4214)
t = -5 seconds. ... ???
So, that means he caught up to the train before he reached his maximum speed. That is,
5.2t = 1/2 * 1.4 * t^2
7.429 seconds