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The equation of motion of a particle sta...

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

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
`X = 5 sin (20 t + (pi)/(3))`
`v = (dx)/(dt) = 100 cos (20 t + (pi)/(3))`
`a = (dv)/(dt) = - 2000 sin (20 t + (pi)/(3))`
(a) `v = 0` for the first time when,
`20 t + (pi)/(3) = (pi)/(2)`
`:. t = (pi)/(120)s`
(b) `a = 0` for the first time, when
`20 t + (pi)/(3) = pi`
`:. t = (pi)/(30)s`
( c) When `a = 0` for the first time, its speed will be maximum. `t = (pi)/(30)s`
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