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\times 10^8 m/s? (b) How far will it travel in so doing?
Solution:
a) To solve this part of the problem, we will use the following equation:
v=v_0+at where v is final velocity, v_0 is initial velocity, a is acceleration, and t is time.
Let us isolate for t and substitute the values given to us in the problem.
t=\frac{v-v_0}{a}
t=\frac{3.0\times 10^7 m/s-0}{9.8 m/s^2}
t=3.1\times 10^6 s
b) To determine the distance traveled by the rocket during this time, we can use the following equation:
x=x_0+v_{0}t+\frac{1}{2}at^2 where x is final displacement, x_0 is initial displacement, t is time, and a is acceleration.
Isolating for x and substituting the values we are given gives us:
x=\frac{1}{2}(9.8 m/s^2)(3.1\times 10^6s)^2
x=4.6\times 10^{13}m.
This question can be found in Fundamentals of Physics, 10th edition, chapter 2, question 31.
