The acceleration of a car moving along a straight road at time t seconds is a(t)=3t2−18t+24.
a. (i) Write the condition on a(t) that must hold for the velocity to be increasing.
b. (ii) Find the interval(s) of time for which the velocity of the car is increasing.
c. (iii) Interpret your answer for part (ii) in one sentence about the car's motion.