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?

Question

Philoid · Accepted Answer

(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.

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?

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?