A body of mass 1 kg starts moving from rest `t = 0` in a circular path of radius 8 m. Its kinetic energy varies with time as `k = 2t^(2) J` then magnitude of centripetal acceleration ( in `m//s^(2)` ) at `t = 2s` is.

Answer

2

Explanation

`(dk)/(dt) = 4t`
`dk = 4t dt = F.ds`
`4t dt = a_(T) ds`
`underset(0)overset(t)int 4t dt = underset(0)overset(v)int v dv`
`(4t^(2))/(2) = (v^(2))/(2) " " at t = 2s`
`rArr v = 2t " " v = 4 m//s`
`a_(c ) = v^(2)//R = 4^(2)//8 = 2 m//s^(2)`