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Q.
Is the work required to be done by an external force on an object on a frictionless, horizontal surface to accelerate it from a speed $v$ to a speed $2v$
Work, Energy and Power
Solution:
The net work needed to accelerate the object from $v = 0$ to $v$ is
$W_{1}=K E_{1 f} -K E_{1 i}$
$=\frac{1}{2} m v^{2}-\frac{1}{2} m(0)^{2}$
$=\frac{1}{2} m v^{2}$
The work required to accelerate the object from speed $v$ to speed $2v$ is
$W_{2} =K E_{2 f}-K E_{2 i}$
$=\frac{1}{2} m(2 v)^{2}-\frac{1}{2} m v^{2}$
$=\frac{1}{2} m\left(4 v^{2}-v^{2}\right)$
$=3\left(\frac{1}{2} m v^{2}\right)=3 W_{1}$