Can you accelerate faster than the speed of light?

[MrInteresting]

hello all,
I know that it is impossible for something to have a speed greater than c, is it possible however to accelerate faster than c? For example, would it be possible to accelerate something at 4c/s for 1/8 of a second, resulting in a speed of 1/2c?

 

[Dale]

Acceleration and speed have different units, you cannot compare them.

 

[ghwellsjr]

There's no limit on the magnitude of "a" but the resulting speed change is less than "at".

 

[MrInteresting]

Acceleration and speed have different units, you cannot compare them.

im not comparing them to each other. I am asking if acceleration has a limit, using the limit of v=c as an example.

There's no limit on the magnitude of "a" but the resulting speed change is less than "at".

This isn't clear to me, at=v, did you mean at<c?

 

[grav-universe]

The relativistic formula for the speed attained according to the rest frame is

$v/c=(at/c)/sqrt(1+(at/c)^2)$

Plug in any values you want for the constant proper acceleration and the length of time of acceleration according to the rest frame and the resulting speed will always be less than c.

 

[yuiop]

hello all,
I know that it is impossible for something to have a speed greater than c, is it possible however to accelerate faster than c? For example, would it be possible to accelerate something at 4c/s for 1/8 of a second, resulting in a speed of 1/2c?

Broadly speaking the upper limit to the acceleration is infinite and certainly greater than 1c/s^2. The correct equation for the terminal velocity due a given constant proper velocity has been given by grav-universe. The choice of 1 seconds as the time unit for acceleration is arbitrary and we can always find a smaller unit of time where the speed of light limit is not broken in that time. What is debatable is whether there is a limit imposed by quantum considerations such as the maximum velocity attainable in one Planck unit of time, which depends upon whether the Plank unit is an indivisible "quanta" of time, but since no experiments have ever been carried out in these extremes, I would be moving into the realm of pure conjecture. Consider it just an idle thought Maybe we will learn more when someone comes up with a true Theory of Everything and quantum gravity, but as far as I know, SR and GR do not put an upper limit on acceleration.

 

[ghwellsjr]

There's no limit on the magnitude of "a" but the resulting speed change is less than "at".

This isn't clear to me, at=v, did you mean at<c?

No, I was taking what I thought you were doing in your example:

For example, would it be possible to accelerate something at 4c/s for 1/8 of a second, resulting in a speed of 1/2c?

I thought you had a=4c/s and t=1/8 s and you multiplied according to v=at to get v=1/2 c and I was pointing out that the speed would be less than 0.5c. In fact, using grav-universe's formula it comes out to 0.447c.