At maximum speed assume aerodynamic drag is the dominant retarding force, then we have the work done by the engine when the car moves through a distance is:If the power output from the engine is doubled, then the maximum speed of the car:
B)increase by a factor of sqrt.(2)
C)is also doubled
D)increase by a factor of four
so the power required is the rate at which work is done so if the time to move through is :
Now we are told to (erroneously) assume that , so:
So doubling the power will support a maximum speed times what it was before.