Afugitive tries to hop on a freight train traveling at a constant speed of 5.5 m/s. just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 4.2 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? m

Let the Fugitive catch the empty box after "t" s of time

So the distance moved by train in same time will be

Now in the same way distance moved by fugitive who is accelerating with a = 4.2 m/s^2 to his maximum speed v = 8 m/s

SO the time taken by him to reach maximum speed

distance moved by fugitive in t = 1.9 s

So in 1.9 s the train will move more than 7.62 m so it will definitely catch the train after this

distance moved by fugitive in time "t" = distance moved by train in same time

Let say it will catch the train after t = 1.9 s so after that time it will move to his constant speed of 8 m/s

So it will take 3.03 s to catch the train

Part B)

Distance traveled by fugitive in same time

here it is because the fugitive will accelerate to reach at his maximum speed of 8 m/s till 1.9 s and cover a total distance of 7.62 m and after that it will move at his maximum speed for rest of the time.

so it will move a distance of 16.67 m