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`

Options

A. equal to the work required to accelerate the object from `t = 0` to `v`.
B. twice the work required to accelerate the object from `v = 0` to `v`.
C. three time the work required to accelerate the object from `v = 0` to `v`.
D. four time the work required to accelerate the object from ` 0` to `v`. Or

Answer

C

Explanation

The net work needed to accelerate the object from `v= 0` to `v` is
`W_(1) = KE_(1 f) - KE_(1 i) = (1)/(2) mv^(2) - (1)/(2) m (0) ^(2) = (1)/(2) mv^(2)`
The work required to accelerate the object from speed `v` to speed `2 v` is
`W_(2) = KE_(2 f) - KE_(2 i) = (1)/(2) m(2 v)^(2) - (1)/(2) mv^(2)`
` = (1)/(2) m (4 v^(2) - v^(2)) = 3 ((1)/(2) mv^(2)) = 3 W_(1)`