(a)  To make a plot, go to website  www.desmos.co./calculator

     Find there an online plotting tool, free of charge for common use.

     Print your given function for velocity and get the plot immediately.



(b)  The displacement of the particle from t= 0 to t =  is the integral

     from  0  to    of the velocity, which is cos(t).

     Function cos(t) is zero at t=   and is odd-symmetric about this point t= .

     It implies that the integral of cos(t) from 0 to   equals to 0 (zero).

     Thus the displacement under the question (b) is zero.

     It means that at t=   the particle returns to the initial point.



(c)  The total distance traveled by the particle from t= 0 to t =  is the integral

     from  0  to    of function  |cos(t)|   (notice the absolute value sign).

     Function cos(t) is zero at t=   and is odd-symmetric about this point t= .

     It implies that function  |cos(t)| is an EVEN function about the point t= .

     Hence, integral of  |cos(t)|  from 0 to   equals to doubled integral of function cos(t) 
     from  0 (zero)  to  .

     Integral of function cos(t) from  0 (zero)  to   is  1-0 = 1.

         //Notice that anti-derivative for cos(t) is sin(t). //


     Thus the total distance traveled by the particle under question (c) is  2*1 = 2 units.