Suppose a rocket ship in deep space moves with constant acceleration equal to 9.8 m/s2, 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 × 108 m/s? (b) How far will it travel in so doing?
It starts from rest, and its speed increases by 9.8 m/s every second.
One tenth the speed of light is (1/10) (3 x 10⁸ m/s) = 3 x 10⁷ m/s .
To reach that speed takes (3 x 10⁷ m/s) / (9.8 m/s²) = 3,061,224 seconds .
That's about 35 days and 10 hours.
Distance traveled = (average speed) x (time of travel)
Average speed = (1/2) of (1/10 the speed of light) = 1.5 x 10⁷ m/s .
Time of travel is the answer to part (a) above.
Distance traveled = (1.5 x 10⁷ m/s) x (3,061,224 sec) = 4.59 x 10¹³ meters
That's 45.9 billion kilometers.
That's 28.5 billion miles.
That's about 6.2 times the farthest distance that Pluto ever gets from the Sun.