The velocity v reached by a car of mass m at certain distance from the starting point driven with constant Power P is such that

Options

A. `v alpha(3P)/(m)`
B. `v^(2)alpha(3P)/(m)`
C. `v^(3)alpha(3P)/(m)`
D. `v alpha((3P)/(m))^(2)`

Answer

c

Explanation

Power,` P=F.v=ma.v=m,dv/ds.v=mv^(2)dv/ds`
therefore `v^(2)dv=(p)/(m)ds ` applying integration on both sides, we get ,
`int v^(2)dv=int(p)/(m)ds`
therefore `(v^(3))/(3)=P/(m).s`
therefore `v^(3) alpha 3p/m`