The position of a particle moving along a straight line is given by s(t)=3t3−12t2+9t+5 metres, where t is the time in seconds (1≤t≤3).
a. (i) Determine the average velocity of the particle during the time interval [1,3].
b. (ii) Find the expression for the instantaneous velocity v(t).
c. (iii) Calculate all values of t in the open interval (1,3) for which the instantaneous velocity equals the average velocity obtained in part (i).
d. (iv) Compute the acceleration of the particle at each value of t found in part (iii) and state whether the particle is speeding up or slowing down at that instant.