$\"\"$

\

A particle is moving with a acceleration $\"\"$ , $\"\"$ and $\"\"$ .

\

The acceleration of the object is $\"\"$ , where $\"\"$ is the velocity.

\

Hence $\"\"$ .

\

The anti derivative of $\"\"$ is $\"\"$ .

\

The anti derivative of $\"\"$ is $\"\"$ .

\

The antiderivative of $\"\"$ is

\

$\"\"$

\

$\"\"$ , where $\"\"$ is the constant.

\

Here $\"\"$ .

\

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

\

$\"\"$

\

Therefore the velocity of the object is $\"\"$ .

\

$\"\"$

\

The velocity of the object is $\"\"$ .

\

The velocity of the object is $\"\"$ , where $\"\"$ is the distance.

\

Hence $\"\"$ .

\

The antiderivative of $\"\"$ is

\

$\"\"$

\

$\"\"$ , where $\"\"$ is the constant.

\

Here $\"\"$ .

\

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

\

$\"\"$

\

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

\

$\"\"$

\

Therefore the position of the particle is $\"\"$ .

\

$\"\"$

\

The position of the particle is $\"\"$ .