# 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 $v$?

Toolbox:
• 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.
edited Aug 19, 2014