Answer
See work.
Work Step by Step
As seen in equation 6.13, the work-energy theorem, the total work on the object is the change in its kinetic energy.
If we do twice the work, the change in kinetic eneergy is twice as much. It started from rest, so it has kinetic energy of 2K.
If the object has twice the kinetic energy as before, since $K=\frac{1}{2}mv^2$, the speed v will be $\sqrt{2}$ greater than it was before, i.e., the new speed is $v\sqrt{2}$.
