(a)

The position function of the particle is .

The velocity function is the derivative of the position function.

Consider .

Apply derivative on each side with respect to .

Velocity of the particle is  m/sec.

,  and .

Time cannot be negative, hence  is not considered.

At , the particle is at rest.

Consider .

Velocity of the particle is  m/sec at  sec.

(b)

Consider .

Acceleration is derivative of the velocity function.

Find time when acceleration of the particle is zero.

Roots of the quadratic function  are .

Here  and .

Substitute above values in .

Therefore acceleration is zero at  sec.

Velocity reaches maximum after this   sec and thereafter moves with constant velocity. 

(a) Velocity of the particle is  m/sec at  sec.

(b) The acceleration is zero at  sec.

Velocity reaches maximum after this   sec and moves with constant velocity.