Question

A fugitive tries to hop on a freight train traveling at a constant speed of 5.4 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 6.1 m/s , which he then maintains. How long does it take him to catch up to the empty box car? What is the distance traveled to reach the box car?

Answer 1

maximum speed of fugitive = V = 6.1 m/sec

   acceleration = a = 1.4 m/sec^2

time = t = V / a = 6.1 / 1.4 = 4.357 = 4.36 sec

in this time distance travelled by fugitive = S = V0 * t + 1/2 * a * t^2

                                                             S = 0 + 1/2 * 1.4 * 4.36^2 = 13.3 m
distance travelled by train = St = 5.4 * 4.36 = 23.54 m

difference in distance = 23.54 - 13.3 = 10.24 m
difference in velocity = 6.1-5.4 = 0.7 m/sec
                 time = 10.24 / 0.7 =14.63 sec
time to catch the box car = 4.36 + 14.63 = 18.98 sec
distance = 18.98 * 4.36 = 82.7 m