Physics question

[Kinofp]

So I have a rocket that accelerates constantly from 0 to 45% the speed of light. I know that it has to travel 6 light years from Earth to Barnard's Star.

I need to know how long it takes for the rocket to get there and I need to know how long it appears to take from an observer on Earth.

Is there any more information I need? (if I need the ship's mass, I'm screwed)

If nobody wants to do the math for it can someone at least direct me to the equation I need? THANKS.

[IronsightSniper]

How fast is it accelerating?

[Arcadian Empire]

You need the time dilation equation.

[deathbiter]

You have to use 2 equations the first one is V^2=Vo^2 +2a(X-Xo)
V= final velocity = 135000000 m/s
Vo= initial velocity = 0 m
a=acceleration = ?
X=final distance = 5.67 * 10^16 m
Xo= initial distance = 0
The second equation is V=Vo +aT
V= final velocity = 135000000 m/s
Vo= initial velocity = 0
a= acceleration = 0.160714286 m/s/s
T=time ? in seconds
The final answer that I came up with is 26.63622522 years. This is not taking into account the force of gravity of the stars and the planets. As for the second part my guess is just add 6 years to the above number since that is how long it would take for light to reach Earth from that distance. You might want to check my math yourself and make sure I did everything correctly but it should be correct.

[Kinofp]

Originally Posted by deathbiter

You have to use 2 equations the first one is V^2=Vo^2 +2a(X-Xo)
V= final velocity = 135000000 m/s
Vo= initial velocity = 0 m
a=acceleration = ?
X=final distance = 5.67 * 10^16 m
Xo= initial distance = 0
The second equation is V=Vo +aT
V= final velocity = 135000000 m/s
Vo= initial velocity = 0
a= acceleration = 0.160714286 m/s/s
T=time ? in seconds
The final answer that I came up with is 26.63622522 years. This is not taking into account the force of gravity of the stars and the planets. As for the second part my guess is just add 6 years to the above number since that is how long it would take for light to reach Earth from that distance. You might want to check my math yourself and make sure I did everything correctly but it should be correct.

Thanks for going through this.

I'm not a pro at physics, but do these equations take relativity into account? It looks like they're Newtonian (but please prove me wrong).

[Arcadian Empire]

I need to know how long it appears to take from an observer on Earth.

For that part, you need the time dilation equation - I believe.


The other part - not sure, because that wasn't in the Physics I did in high school.

[Kinofp]

Is it this?

[deathbiter]

"I'm not a pro at physics, but do these equations take relativity into account? It looks like they're Newtonian (but please prove me wrong)."

I am not exactly sure what you mean by the above, but these equations along with another one are the ones that I learned at the start of the year in my physics class. They are used to describe motion in one dimension (a straight line) with a constant acceleration.