Answer:
[tex]\sqrt{2}v[/tex]
Explanation:
The work done on the object at rest is all converted into kinetic energy, so we can write
[tex]W=\frac{1}{2}mv^2[/tex]
Or, re-arranging for v,
[tex]v=\sqrt{\frac{2W}{m}}[/tex]
where
v is the final speed of the object
W is the work done
m is the object's mass
If the work done on the object is doubled, we have W' = 2W. Substituting into the previous formula, we can find the new final speed of the object:
[tex]v'=\sqrt{\frac{2W'}{m}}=\sqrt{\frac{2(2W)}{m}}=\sqrt{2}\sqrt{\frac{2W}{m}}=\sqrt{2}v[/tex]
So, the new speed of the object is [tex]\sqrt{2}v[/tex].
