An object moves along a straight line in such a way that its position at time t is given by

a. What are the object’s velocity v(t) and acceleration a(t) at time t?

b. When is the object stationary for 0 ≤ t ≤ 2? Where is the object and what is its acceleration at each such time?

c. When is the acceleration zero for 0 ≤ t ≤ 2? What are the object’s position and velocity at each such time?

d. Use the graphing utility of your calculator to draw the graphs of the object’s position s(t), velocity v(t), and acceleration a(t) on the same screen for 0 ≤ t ≤ 2.

e. The object is said to be slowing down when v(t) and a(t) have opposite signs (one positive, the other negative). Use your calculator to determine when (if ever) this occurs for 0 ≤ t ≤ 2.

s(t)=(3+t-12)3/2 for 0 t 2