Answer the following questions for the displacement function ?(?)= t²e^-t where s is measured in feet, and t is measured in seconds.

(a) Find the velocity at time t. (b) What is the velocity after 3 s? (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (e) Find the total distance traveled during the rst 8 s. ( f) Draw a diagram like Figure 2 to illustrate the motion of the particle. (g) Find the acceleration at time tand after 3 s. a (h) Graph the position, velocity, and acceleration functions for 0 S t S 8. (i) When is the particle speeding up? When is it slowing down