Step 1:

The derivative function is  and .

Integration of derivative function results the function it self. 

Consider .

Integrate on  each side with respect to .

Integral formulae:

and 

.

We have .

Substitute in .

Substitute in .

.

Step 2:

A particle moves in a straight line.

Acceleration  of the  particle is and

Initial velocity is cm/s.

Initial displacement cm.

Anti derivative of the acceleration function is velocity.

.

Integrate on  each side with respect to .

We have, .

Substitute in .

Substitute in .

.

Anti derivative of the velocity function is position function.

. 

Integrate on  each side with respect to .

.

.

Power rule of integration : and .

We have, .

Substitute in .

Substitute in .

.

Position function of the particle .

Solution:

1) .

2)  Position function of the particle .