A particle moves along a straight track so that its position, measured in meters from a fixed origin, is given for 0 \le t \le 5 seconds by the function
s(t)=4t2−12t+7.
Answer the following questions about the motion of the particle.
(a) Determine the particle’s velocity v(t) for 0≤t≤5. Give appropriate units.
(b) Evaluate the instantaneous velocity at t=1.5 seconds and interpret its sign in terms of the particle’s direction of motion.
(c) Compute the average velocity of the particle on the interval 1≤t≤3.
(d) Explain, using your results from parts (b) and (c), whether the particle changed direction during the interval 1≤t≤3. Justify your conclusion.