Time traveled under constant acceleration.

[mickleroi]

Homework Statement

I am doing some study for a short sci-fi story I'm writing. I'm trying to figure out how to determine the time that a craft has traveled if I know the constant acceleration and distance traveled.
eg. A ship accelerates constantly at 1g and travels 0.5 light years. How long did this the ship take to travel that distance?

Homework Equations

I have found the following equation which finds distance traveled based on constant acceleration and time, but I am having trouble making t the subject.

s=v0t+at^2/2

The Attempt at a Solution

As mentioned above I have tried to change the subject of the formula, but to no avail.

 

[PeterO]

Homework Statement

I am doing some study for a short sci-fi story I'm writing. I'm trying to figure out how to determine the time that a craft has traveled if I know the constant acceleration and distance traveled.
eg. A ship accelerates constantly at 1g and travels 0.5 light years. How long did this the ship take to travel that distance?

Homework Equations

I have found the following equation which finds distance traveled based on constant acceleration and time, but I am having trouble making t the subject.

s=v0t+at^2/2

The Attempt at a Solution

As mentioned above I have tried to change the subject of the formula, but to no avail.

The trouble you may find is that if 1 g acceleration [presumably you mean 9.8 ms^2] was maintained over that distance, the craft would be traveling faster than the speed of light - an indication that it could not accelerate at that rate over the whole distance, and also you would be moving into the area of Einstein's postulates rather than continuing to use Newton's Laws of motion.

Of course it is science fiction - so you could just make it up. The equations will have the craft exceeding the speed of light, thus averaging about half the speed of light (slightly over), so will take about half a year (slightly less).

 

[SteamKing]

It's a quadratic equation in t. You have studied quadratic equations before?

 

[mickleroi]

PeterO, I should have mentioned in my original post - as this is for a sci-fi story I have made up a way around the light speed limit, so I don't need to worry about relativistic effects or physical limitations on acceleration.

SteamKing, I haven't studied quadratic equations since high school. That's ten years ago now, so i suppose I might need to brush up on that...

 

[PeterO]

PeterO, I should have mentioned in my original post - as this is for a sci-fi story I have made up a way around the light speed limit, so I don't need to worry about relativistic effects or physical limitations on acceleration.

SteamKing, I haven't studied quadratic equations since high school. That's ten years ago now, so i suppose I might need to brush up on that...

With no "speed limits" you can make better use of other equations of motion under constant acceleration to get a feel for the situation

eg. If you are starting from rest,

the distance traveled is half the final speed multiplied by time

The square of the final speed = 2 x acceleration x distance.

As I said, that second formula yields a final speed just over the speed of light after accelerating over a 0.5 light year distance, so taking about 0.5 years to get there.

 

[mickleroi]

Ah, those formulae work a treat! I'm getting 508.5 days to travel 1ly under constant 1g acceleration and a final speed of 1.44c. Seems about right to me!

Thanks So much for your help!