Question

A fugitive tries to hop on a freight train traveling at a constant speed of 5.0 m/s. Just as an empty box car passes him, the fugitive starts from rest and accelerates at a = 4.0 m/s²to his maximum speed of 8 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

Answer 1

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. If this helps then kindly rate 5-stars.

A fugitive tries to hop on a freight train traveling at aconstant speed of 5.0 m/s. Just as an empty box car passeshim, the fugitive starts from rest and accelerates at a = 1.2m/s² to his maximum speed of 6.0 m/s. (a) How long doesit take him to catch up to the empty box car?

(b) What is the distance traveled to reach the box car?

a)

let the time be t, we have:

for the box car distance is : d2 = vt (where v =5.0m/s)

since max speed is u = 6.0m/s and takes t2 to reach:

u = 6.0m/s = 1.2m/s²*t2 =>t2 = 5s

distance to catch up d1 = (1/2)a (t2)²  + u*(t-t2) =(1/2)*1.2m/s²*(5s)² + 6.0m/s*(t-5)

              =15 m + 6.0t - 30.0m = -15.0m+6.0t

d1 = d2 => -15.0m + 6.0t = vt = 5.0t

=>t = 15.0s, it take 15.0s to catch up

b)

the distance is d2 = 5.0m/s*15.0s = 75.0m