The displacement of a particle moving in a straight line depends on time as `x=alpha t^(3)+beta t^(2)+gamma t+delta`. The ratio of initial acceleration to its initial velocity depends

Options

A. The particle never returns to its starting point
B. The particle comes to rest after time `(2alpha)/(3beta)`
C. The initial velocity of the particle is zero
D. The initial acceleration of the particle is zero

Answer

D

Explanation

x= 0 at t = 0 and `t = alpha//beta`. So, the particle returns to starting point at `t=alpha//beta`.
`upsilon=(dx)/(dt)=2alpha t-3beta t^(2)`
At t = 0, `upsilon = 0` i.e., initial velocity of particle is zero.
`upsilon=0` at t = 0 and `t=(2alpha)/(3beta)`
Thus, the particle comes to rest after time
`t=2alpha//3beta rArr a=(d upsilon)/(dt)=2alpha-6beta t`
At `t=0, a=2, a ne 0`