Russ P. answered • 10/07/14
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Sam,
In the simplest case of a constant force F over time, and a constant mass M over time, Newton's Law states F = Ma, where a is the acceleration, which is now also constant with time.
And we also know the distance traveled formula, x = vt. The derivative of x with respect to time is dx/dt = v or velocity. Furthermore, the second derivative of x then equals the first derivative of v which is just acceleration a.
So d2x/dt2 = dv/dt = a.
Putting all this together: a= F/M = d2x/dt2
Or solving it for x, x= (F/2M)t2 assuming velocity and distance were zero at time zero.
This shows how the mass M affects distance x.
Russ P.
Sam,
Then that is a constraint you should state in the question to guide those answering.
Answer now: The larger the mass, the heavier it becomes (gravity pulling on it), the slower and shorter distance it can be moved if the force is not changed. Or, massier, heavier objects require greater pushing (Force) to move them faster or farther.
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10/07/14
Sam C.
Thank you! I really appreciate it. :)
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10/07/14
Sam C.
10/07/14