A particle moves according to a law of motion s = Ft), t2 0, where t is measured in seconds and 's in feet." fit) = 13 _ 122 + 36t (a) Find the velocity at time t (in ft/s).v(t) = (b) What is the velocity (in ft/s) after 3 s? v(3) = ft/s When (in seconds) is the particle at rest?(smaller value) t = (larger value) t When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance (in feet) traveled during the first 8 s. ft (f) Find the acceleration at time t (in ft/s2). a(t) = Find the acceleration (in ft/s2) after 3 s. a(3) = A/s? (g) Graph the position, velocity, and acceleration functions for the first 8 s. 8