The motion of a particle along a straight line is described by the equation: `x=8+12t-t^(3)`, where `x` is inmeter and `t` in second.
(i) the initial velocity of particle is 12 m//s
(ii) the retardation of particle when velocity is zero is `12 m//s^(2)`
(iii) when acceleration is zero, displacement is 8 m
the maximum velocity of particle is `12 m//s`

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (ii), (iii)
D. All option are correct

Answer

D

Explanation

`x=8+12t-t^(3)`
`v=12-3t^(2)`
`a=-6t`
At `t=0, v=12 m//s`, (i) is O.K.
When `v=0=12-3t^(2)impliest=2 s`
`a=-6t=-12 m//s^(2)`, (ii) is O.K.
When `a=-6t=0impliest=0`
At `t=0, x=8 m`, (iii) is O.K.
The velocity will be maximum, if
`(dv)/(dt)=a=-6t=0impliest=0`
At `t=0, v=v_(max)=12 m//s`, (iv) is O.k.