To simulate artificial gravity, a spaceship accelerates through space at 9.8 m/s2 . a) if it starts from a stop, how long (in time) will it take to reach a speed of 0.1c where c is 3 x 108 m/s (the speed of light). b) how much space does it cover during this time?

(a) Time taken to reach the speed will be

(b) Space cover by spaceship

Explanation:

We have given acceleration due to gravity

As the spaceship starts from rest so initial velocity u = 0 m/sec

Final velocity v = 0.1 c, here c is speed of light

So final velocity

(a) According to first law of motion we know that v=u+gt, here v is final velocity, u is initial velocity and t is time

So

(b) According to third law of motion

The spaceship will take 850.34 hours to reach a speed of 0.1c and it will travel 45 918 367 346.9 km before reaching that speed.

Explanation:

The spaceship is traveling at a constant acceleration, then we can use the kinematic equations for that kind of movement to calculate the time it would take to reach a given speed.

Where is the initial speed, is the acceleration rate and is the speed the spaceship will have at a time .

If the spaceship starts from a stop, then . So:

Then, the spaceship will take 850.34 hours to reach a speed of 0.1c

To calculate the displacement of the spaceship during that time, we use the following equation:

Where is again the initial speed (which is zero), is the acceleration and is the travel time (which we've calculated is the previous step).

Then, the spaceship will travel 45 918 367 346.9 km before reaching a 0.1c speed.

radiation

explanation:

heat is transmitted by radiation