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Hello! I am also wondering, if one was to apply an acceleration that is above the value of "c" on an object to create a force on that object then in that case, wouldn't outside observers as well as the accelerating object agree that it would only take a finite amount of time to reach and surpass the speed of light?
Question Date: 2010-07-15
Answer 1:

You can't apply an acceleration that is "above" c. The speed of light is a velocity; it has units of distance (meters) per time (seconds). Acceleration has units of distance per time SQUARED. You can't directly compare acceleration and a velocity, unless you talk about acceleration applied over a period of time.

Acceleration is by definition the rate of change in an object's momentum (i.e. force) divided by its mass. There is an equation in special relativity that gives you the ratio of an object's rest mass to its relativistic mass. If you know the acceleration, and the amount of time over which the acceleration was applied, you can do some algebra with that equation and the above definition and the mass of the object will cancel out allowing you to solve for the velocity. The velocity will of course be less than c, because the momentum of the object becomes infinite as the velocity approaches c.

If you want to know the instantaneous rate of change in an object's observed velocity (i.e. its acceleration as measured by a stationary observer), given the acceleration the object is experiencing in its own reference frame, then you need to do some calculus (specifically, you need to evaluate the derivative of the relativistic equation at the desired velocity).

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