Free Fall/Constant Acceleration Problem

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A rocket ship accelerates at 9.8 m/s² from rest to reach one-tenth of the speed of light, which is 30,000,000 m/s. The calculations initially provided resulted in a time of approximately 3,061,224.49 seconds and a distance of 4.59 x 10^13 meters. However, the time calculation was incorrect due to a decimal error, which also affected the distance result. The correct approach involves careful attention to decimal placement in the equations for velocity and distance. Accurate calculations are essential for solving physics problems involving constant acceleration.
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Homework Statement


A rocket ship in free space travels with a constant acceleration equal to 9.8m/s^s.
a)If it starts from rest how long does it take to reach a velocity of one tenth of the speed of light? Note: The speed of light in a vacuum is 3.0 x 10^8 m/s.
b)How far will it travel during this time?


Homework Equations


V=Vo+at
X=Xo+Vot+(1/2)(a)(t)


The Attempt at a Solution


I started with making a variable list:
a=9.8 t=?
Vo=0 Xo=0
V=30,000,000 X=?

I plugged these values into the equation I mentioned in # 2.
The answers I got are:
a) 3061224.49sec
b)4.59 x 10^13
I wasn't sure how to do this and gave it a shot. Could you please explain.
Thanks!
 
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Your method is fine, but be careful with decimal points. Your answer for (a) is off by a factor of 10, making (b) off by a factor of 100.
 

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