The motion of a particle is described by the equation `x = at^(2)`+`bt^(3)` where `a = 15` cm and `b = 3 cm//s^2`. Its instantaneous velocity at time 5 sec will be

Answer

A, D

Explanation

`x=t^(3)-3t^(2)-9t+5. x(5) gt 0` and `x(3) gt 0`
so `[A] v=dx//dt=3t^(2)-6t-9`
`rArr t=-1, 3` so `t=3`
Hence particle reverses its direction only once average acc.= change in velocity `//`time.
In interval `(t=3 " to " t=6)`, particle does not reverse its velocity and also moves in a straight line so distance =displacement.