How about this?

Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s^2, 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 one-tenth that of light, which travels at 3.0 x 10^8 m/s?
b. How far will it travel in so doing?

1 Answer
Harish Chandra Rajpoot
Jul 2, 2018

85.034\ \text {hrs}

4.588164\times 10^{13}\ m

Explanation:

The time required to achieve a velocity v=1/10\cdot 3\times10^8=3\times 10^7\ m/s from rest u=0 under an acceleration a=9.8\ m/s^2

v=u+at

3\times 10^7=0+9.8t

t=3.06\times 10^6\ s

t=85.034\ \text {hrs}

The distance s traveled by the rocket ship starting from rest u=0 in time t=3.06\times 10^6\ s under an acceleration a=9.8\ m/s^2 is given as follows

s=ut+1/2at^2

s=(0)(3.06\times 10^6)+1/{2}9.8(3.06\times 10^6)^2

=4.588164\times 10^{13}\ m

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