If (t)=3t²-6t-45 for 0≤t≤7 and x(2)= -80,
a. Determine when the object is at rest, moving left and moving right.
b. Express x(t), the position of the object, as a function of t.
c. Set up the definite integrals that will find the total distance traveled by the object for 4≤t≤6
d. Find the acceleration at t = 2