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Let an object be at rest initially and you push it with constant force across a friction-less surface for a time internal $\Delta t$ resulting in a final speed of $v$ for the object. Now, if you repeat the experiment with a force that is twice as large, what will be the time internal needed to reach the same final speed $v$?

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  • Newton's first law states that when viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.
Answer: $0.5 \Delta t$
Twice the force $\rightarrow$ Twice the acceleration.
Since force is constant, acceleration is constant and the speed of the object starting from rest is given by $v = a t$
Now, with twice the acceleration, the object will arrive at half the time required for the speed to be the same in both cases.
answered Aug 19, 2014 by balaji.thirumalai
edited Aug 19, 2014 by balaji.thirumalai

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