A particle moves along the x-axis in such a way that its position at time t is given by x(t) = 2t^3- 15t^2 +36t for t is less than or equal to 0, where x is measured in meters.
a. Determine the velocity and acceleration of the particle at time t.
b. At what value(s) of t is the particle at rest?
c. At what value(s) of t is the particle moving to the left?
d. What is the acceleration of the particle the first time its velocity is zero?
e. Find the position of the particle the first time its velocity is zero.
f. Find the displacement of the particle during the first 5 seconds.
g. Find the total distance traveled by the particle during the first 5 seconds?