A fugitive tries to hop on a freight train traveling at a constant speed of 5.0

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 = 1.3 m/s2 to his maximum speed of 5.8 m/s , which he then maintains. PART A : How long does it take him to catch up to the empty box car? Express your answer to two significant figures and include the appropriate units. PART B : What is the distance traveled to reach the box car? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

given

speed of 5.0 m/s

a = 1.3 m/s2

maximum speed of 5.8 m/s

a )

t = v / a

= 5.8 / 1.3

t = 4.461 sec

the distance moved is 5 X 4.461 = 22.305 m

fugitive moved is = 1/2 a t2 = 0.5 X 1.3 X 4.4612

= 12.935 m

fugitive need to move distance is = 22.305 - 12.935 = 9.37 m

now at 5.8 - 5 = 0.8 m/s

so 9.37 / 0.8 = 11.71 sec

so the time need is = 4.461 + 11.71 = 16.171 sec

then the distance is travelled is = 5 X 16.171

= 80.855 m

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