A particle moves according to a law of motion s = f(t) =. te t/ 5, t2 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. v ( t ) = ft/s (b) What is the velocity after 8 s? (Round the answers to three decimal places.) V (8) = ft/s (c) When is the particle at rest? t = (d) When is the particle moving in the positive direction? (If you need to use -co or co, enter -INFINITY or INFINITY.) (e) Find the total distance traveled during the first 12 s. feet (f) Draw a diagram to illustrate the motion of the particle. (Do this on paper. Your instructor may ask you to turn in this graph.) (g) Find the acceleration at time t and after 8 s. (Round the second answers to three decimal places.) a(t) = a (8) = ft / 52 (h) Graph the position, velocity, and acceleration functions for t 2 0. (Do this on paper. Your instructor may ask you to turn in this graph.) (i) When is the particle speeding up? (If you need to use -co or co, enter -INFINITY or INFINITY.) When is it slowing down? (