Suppose a rocket ship in deep space moves with constant acceleration equal to 9.

Question

Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s, which gives the illusion of normal gravity during the flight. (a) If it starts from rest, how long will it take to acquire a speed 0.15 times that of light, which travels at 3.0 x 108 m/s? (b) How far will it travel in so doing? X km Constant-acceleration equations: You have the initial and final speeds and the acceleration, and you first want the time. Then to find the distance, you have a choice of equations to use

Explanation / Answer

Initial velocity u = 0 (starts from rest)

acceleration a = 9.8 m/s2

final velocity v = 0.15 X 3 X 108 = 4.5 X 107 m/s

using first equation of motion we have

v = u + at

4.5 X 107 = 0 + 9.8 t

t = 4.5 X 107 / 9.8

t = 4.59 X 106 s

using second equation of motion we have

S = ut + (1/2)at2

S = 0 + 0.5(9.8)(4.59 X 106)2

S = 1.03 X 1014 m

S = 1.03 X 1011 Km

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