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?

Options

A. `(pi)/(90)` sec
B. `(pi)/(120)` sec
C. `(pi)/(60)` sec
D. `(pi)/(30)` sec

Answer

D

Explanation

Initial phase `phi_(1) = (pi)/(3)`
final phase `phi_(2) = pi` (acc becomes zero at mean)
`Delta phi = pi - (pi)/(3)`
w.r.t `= (2pi)/(3) rArr 20 xx t = (2pi)/(3)" "t = (pi)/(30)s`