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 = 2.5 m/s2 to 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?

Th equations to be used here are the following:

a = (v - v₀)/t
x = v₀t + 0.5at²

The speed of the fugitive is the sum of his own speed plus the speed of the train. Thus, 
v₀ = 0 + 5.5 m/s = 5.5 m/s
v = 8 m/s + 5.5 m/s = 13.5 m/s

a.) We use the first equation to determine time
2.5 m/s² = (13.5 m/s - 5.5 m/s)t
Solving for t,
t = 3.2 seconds

b.) We use the answer in a) and the 2nd equation:

x = (5.5 m/s)(3.2 s) + 0.5(2.5 m/s²)(3.2 s)²
x = 30.4 meters