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# Physics/Accelerating a greater distance

Question
QUESTION: Does it take a greater force to accelerate an object a greater distance through space in the same amount of time.  Such as accelerating a track with a train moving on it.

ANSWER: In the same amount of time?  I assume you mean from rest, in which case the answer is yes.

---------- FOLLOW-UP ----------

QUESTION: If it takes a greater force to accelerate an object a greater distance through space in the same amount of time , such as a track with a train moving on it; then would it be true that it takes more force to accelerate a moving object in the same amount of time?

You're making a comparison, so your language doesn't quite apply correctly.  Force = mass*acceleration.  If you want to accelerate an object, you need a force to match.  If you have a train moving at a constant velocity on a track, it takes a certain force to accelerate the track, and an additional force to accelerate the train.  Unless you can formulate the problem more clearly, I can't formulate the answer more clearly.  If you're talking about a greater force to accelerate a train that's already moving on a track vs. a force to accelerate one from rest on the track, then no.  Force (at speeds not near the speed of light) is still equal to mass*acceleration.

Perhaps you can clarify.  What are you applying the force to?  The train, or the track?  Are you asking if you need to apply more force to a train in order to accelerate the train that is already moving, as opposed to one starting from rest?  If so, the answer is no.  You apply a force, you get an acceleration independent of the initial velocity of the train.  You have to do more work (spend more energy) for the initially moving train, since you will have to apply it over a greater distance to achieve the same final velocity.

Physics

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#### Dr. Stephen O. Nelson

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