The captain orders his starship to accelerate from rest at a rate of "1 g" (1 g = 9.8 m/s2). how many days does it take the starship to reach 5% the speed of light?
(light travels at 3.0 × 10^8 m/s.)

17.7 days

Explanation:

Since the ship accelerates from the rest, its initial velocity would be equal to 0.

So,

Acceleration of the star-ship = a = 1 g = 9.8 m/s²

We need to find how many days will it take the ship to reach 5% of the speed of light. Speed of light is m/s.

5% of the speed of light = m/s

This means, the final velocity of the star-ship will be:

We have the initial velocity, final velocity and the acceleration. We need to find the time(t). First equation of motion relates these quantities as:

Using the values in this equation, we get:

Thus, the star-ship will take 1,530,612.245 seconds to reach to 5% the speed of light. Now we need to convert this time to days.

Since, there are 60 seconds in a minute:

1,530,612.245 seconds = minutes

Since, there are 60 minutes in an hour:

25,510.20 minutes = hours

Since, there are 24 hours in a day:

425.17 hours = days

Thus, it will take approximately 17.7 days (approximately 17 days and 17 hours) to reach to 5% the speed of light