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.