The equation of motion of a particle started at `t=0` is given by `x=5sin(20t+pi//3)` where x is in centimeter and t in second. When does particle
(a) first come to rest
(b) first have zero acceleration
(c) first have maximum speed?

Explanation

`x=5sin(20t+pi//3)`
`v=(dx)/(dt)=100cos(20t+pi//3)`
(a) When `v=0` i.e., `cos(20t+pi//3)=0cospi//2`
`20t+pi/3=pi/2`
`t=(pi//6)/(20)=(pi)/(120)s`
(b) `a=-omega^2x`, a is zero when `x=0`
`x=0`, when `sin(20t+pi//3)=0=sin0, sin pi`
`20t+pi/3=0impliest:-ve` (not possible)
`20t+pi/3=piimpliest=(2pi//3)/(20)=(pi)/(30)s`
(c) `u` is maximum when acceleration is zero, i.e., `(pi)/(30)s`