A particle moves along straight line acted by a force which delivers power `P=Ct^(7)`. Initially it's velocity is zero. Where C is constant and t is time. Then mark the correct option .

Options

A. displacement of the particle is proportional to `t^(5)`
B. force acting on the particle increases with time.
C. accelertion of the particle is proportional to `t^(3)`
D. rate of change of kinetic energy is proportional to `t^(6)`

Answer

ABC

Explanation

`P=(dW)/(dt)=Ct^(7)`
`1/2 mv^(2)=W=(Ct^(2))/8`
`v=sqrt(C/(4m)t^(4))rArr (dx)/(dt)=sqrt((Ct^(4))/(4m)) rArr `
`x=sqrt(C/(4m)) (t^(5))/5`
`F=(mdv)/(dt)=msqrt(C/(4m))xx4t^(3)`
`(dk)/(dt)=(dW)/(dt)=Ct^(7)`