A constant power `P` is applied to a particle of mass `m`. The distance traveled by the particle when its velocity increases from `v_(1)` to `v_(2)` is (neglect friction):

Options

A. `(3P)/m(v_(2)^(2)-v_(1)^(2))`
B. `m/(3P)(v_(2)^(3)-v_(1)^(3))`
C. `m/(3P)(v_(2)^(2)-v_(1)^(2))`
D. `m/(3P)(v_(2)-v_(1))`

Answer

B

Explanation

acceleration `a=P/(mv)`
`v(dv)/(dx)=P/(mv)`
`int_(0)^(a)dx=m/P int_(v_(1))^(v_(2))v^(2)dv`
`S=m/(3p)(v_(2)^(2)-v_(1)^(2))`