A particle moves along a horizontal line so that its position at any time t ⥠0 is given by s(t) = -t^3+ 7t^2-14t +8 , where s is measured in meters and t in seconds. Required:
a. Find the instantaneous velocity at any time t and when t = 2.
b. Find the acceleration of the particle at any time t and when t = 2.
c. When is the particle at rest? When is moving to the right? To the left? Justify your answers.
d. Find the displacement of the particle during the first two seconds?
e. Find the total distance traveled by the particle during the first two seconds?
f. Are the answers to (d) and (e) the same? Explain.
g. When is the particle speeding up? Slowing down? Justify your answers.