The equation of motion of a particle started at t = 0 is given by x = 5 sin (20 t + π/3), where x is in centimeter and t in second. When does the particle

(a) first come to rest

(b) first have zero acceleration

(c) first have maximum speed?

(a)

(b)

(c)

The give equation is,

(a) the velocity of the particle will be zero at extreme position.

Now,

Taking x = 5(amplitude)

=

.

So at sec it will come to rest for the first time.

b) As we know,

As we know, ,

c)

when, v is maximum

i.e.

1