An older-model car accelerates from `0` to speed `v` in a time interval of `Delta t`. A newer, more powerful sports car accelerates from `0 to 2v` in the same time period. Assuming the energy coming from the engine appears only as kinetic energy of the cars. Choose correct statement.

Options

A. The power of the sports car is four times that of the older-model car.
B. The power of the sports car is two times that of the older-model car.
C. The power of the sports car is equal to that of the older-model car.
D. The power of the sports car cannot be compared from given data.

Answer

A

Explanation

`P= (W)/(Delta p)`
older - model : `W = (1)/(2)mv^(2) rArr p_(older) = (mv^(2)//2)/(Delta t) = (mv^(2))/(2 Delta t)`
newer - model: `W = (1)/(2)m(2v)^(2) = (1)/(2)(4mv^(2))`
`rarr P_(newer) = (4mv^(2))/(2 Delta t) = 4(mv^(2))/(2 Delta t)`
Hence the power of the sports car is four times that of the older - model car.