The relation between time `t` and distance `x` of a particle is given by `t=Ax^(2)+Bx`, where `A` and `B` are constants. Then the
`(A)` velocity is given by `v=2Ax+B`
`(B)` velocity is given by `v=(2Ax+B)^(-1)`
`(C )` retardation is given by `2Av^(2)`
`(D)` retardation is given by `2Bv^(2)`
Select correct statement `:-`

Options

A. Only `C`
B. Only `D`
C. Only `A` & `D`
D. Only `B` & `C`

Answer

D

Explanation

Differentiating `t-Ax^(2)+Bx` w.r.t. time `1=(2Ax+B)vrArrv=(2Ax+B)^(-1)`
Again differentiating w.r.t. time `(dv)/(dt)=(-1)(2Ax+B)^(-2)(2A(dx)/(dt))=-2Av^(2)`
`rArr` Ratardation `=-(dv)/(dt)=2Av^(2)`