Question

A particle is moving along the path given by `y=(C )/(6)t^(6)` (where `C` is a positive constant). The relation between the acceleration (`a`) and the velocity (`v`) of the particle at `t=5sec` is
A. `5a=v`
B. `a=5v`
C. `a=sqrt(v)`
D. `a=v`

Answer 1

`y=(C )/(6)t^(6) rArr v=(dy)/(dt)=Ct^(5)`
`a=(dv)/(Dt)=5Ct^(4)`
`(a)/(v)=(5)/(t)`
So, at `t=5sec`, `(a)/(v)=1 rArr a=v`