"A fugitive tries to catch a freight train traveling at a constant speed of 5.95 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at 3.84 m/s^2 to his maximum speed of 8.23 m/s. How long does it take him to reach the empty box car?"
To solve this problem, I will use the following formulae on motion :(I assume that you have seen and used these before)
where u=initial velocity; v=final velocity; a=acceleration; s=distance; t=time.
Lets suppose the fugitive takes time 't0' before he catches up with the boxcar.
Now, he will catch up with the boxcar ONLY IF the distance travelled by him in time 't0' and the distance travelled by the boxcar(or train) in time 't0' are EQUAL.
The boxcar(train) travels at an constant speed of 5.95m/s. There is no acceleration or change in velocity. So it is easy ...
With excellent explantions, the formulas and workings are shown to arrive at the answers.