Step 1:

The velocity function is $\"\"$ , $\"\"$ .

(a)

Find displacement.

The velocity is defined as change in displacement over a change in time.

$\"\"$ .

$\"\"$

Displacement of the particle is $\"\"$ .

Step 2:

(b)

Find distance.

To find the total distance, velocity is negative from 0 to $\"\"$ where velocity is positive from $\"\"$ to 3

The total distance of the particle over the interval $\"\"$ .

The total distance $\"\"$

$\"\"$

The total distance of the particle is $\"\"$ .

Solution :

(a) Displacement of the particle is $\"\"$ .

(b) The total distance of the particle is $\"\"$ .