Answer:
17.7 days
Explanation:
Since the ship accelerates from the rest, its initial velocity would be equal to 0.
So,
[tex]v_{i}=0[/tex]
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 [tex]3 \times 10^{8}[/tex] m/s.
5% of the speed of light = [tex]0.05 \times 3 \times 10^{8}=1.5\times 10^{7}[/tex] m/s
This means, the final velocity of the star-ship will be:
[tex]v_{f}=1.5\times 10^{7}[/tex]
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:
[tex]v_{f}=v_{i}+at[/tex]
Using the values in this equation, we get:
[tex]1.5 \times 10^{7}=0+9.8(t)\\\\ t=\frac{1.5\times10^{7}}{9.8}\\\\ t=1,530,612.245[/tex]
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 = [tex]\frac{1,530,612.245}{60}=25510.20[/tex] minutes
Since, there are 60 minutes in an hour:
25,510.20 minutes = [tex]\frac{25,510.20}{60}=425.17[/tex] hours
Since, there are 24 hours in a day:
425.17 hours = [tex]\frac{425.17}{24}=17.7[/tex] days
Thus, it will take approximately 17.7 days (approximately 17 days and 17 hours) to reach to 5% the speed of light
