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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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