$\"\"$

\

The distance of a particle is $\"\"$ .

\

Where $\"\"$ is in seconds and $\"\"$ is in meters.

\

The distance is $\"\"$ .

\

(a)

\

Find an equation for velocity of a particle at any point of time.

\

$\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Apply power rule of derivatives : $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

Therefore, the velocity of a particle at any point of time is $\"\"$ .

\

$\"\"$

\

(b)

\

The velocity of particle is $\"\"$ .

\

Find the velocity of the particle for $\"\"$ and $\"\"$ seconds.

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

For $\"\"$ seconds the velocity of a particle is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

For $\"\"$ seconds the velocity of a particle is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

For $\"\"$ seconds the velocity of a particle is $\"\"$ .

\

Therefore, the velocity of the particle for $\"\"$ and $\"\"$ seconds is $\"\"$ and $\"\"$ .

\

$\"\"$

\

(a) The velocity of a particle at any point of time is $\"\"$ .

\

(b) The velocity of the particle for $\"\"$ and $\"\"$ seconds is $\"\"$ and $\"\"$ .