A rocket ship in free space moves with constant acceleration equal to 9.8 m/s2, (a) If it starts from rest, how long will it take to acquire a speed one-tenth that of light? (b) How far' will it travel in so doing? (The speed of light is 3.0 X 108 m/s.)

We assume that the motion is along the x direction only
Given:
Speed of light, c = 3.0 x 10⁸ m/s.
Acceleration of rocket ship, a_x = 9.8 m/s².
Initial speed of rocket ship, v_0x = 0 m/s.
(a) Let us assume that the time taken by the rocket ship to reach the final speed (say _vx) which is one-tenth the speed of light (c)is given by t. Therefore the time t is can be calculated from the definition of the acceleration as:

t = 3.0 x 106 s

Therefore it will take 3.0 x 10⁶ for the rocket jet to reach the speed which is one-tenth the speed of light.
(b) Let us assume that the rocket jet has to travel x meters to reach the speed which is one-tenth the speed of light. Therefore, we can calculate x as:
With initial condition, x₀ = 0, x is given as:

With initial condition, x₀ = 0, x is given as:

Substitute the given values to obtain the value of x as:

Therefore the rocket jet has to travel 4.4 x 10¹³ to attain the speed one-tenth the speed of light.