The dispalcement x of particle moving in one direction, under the action of a constant force is related to the time t by the equation $$t = \sqrt x + 3$$
where x is in meters and t in seconds. Find

(i) The displacement of the particle when its velocity is zero, and

(ii) The work done by the force in the first 6 seconds.

Answer the following giving reason in brief:

Is the time variation of position, shown in the figure observed in nature?