A particle moves according to a law of motion s= f(t), t≥ 0, where t is measured in seconds and s in feet. f(t) = t3 - 12t² + 36t (a) Find the velocity at time t (in ft/s). v(t) = (b) What is the velocity (in ft/s) after 5 s? v(5) = ft/s (c) When (in seconds) is the particle at rest? (smaller value) t = S (larger value) t = (d) When (in seconds) is the particle moving in the positive direction? (Enter your answer using interval notation.) te (e) Find the total distance (in feet) traveled during the first 7 s. ft (f) Find the acceleration at time t (in ft/s²). a(t) = Find the acceleration (in ft/s2) after 5 s. a(5)= ft/s² S (9) Graph the position, velocity, and acceleration functions for the first 7 s. y y 40 20 -20 S 4 6 اہے 8 40 20 -20 4 2 V 4 (h) When, for 0 st<∞, is the particle speeding up? (Enter your answer using interval notation.) When, for 0 ≤ t < , is it slowing down? (Enter your answer using interval notation.) 6 8 t y 40 20 -20 2 4 6 8 t y 40 20 -20 # 2 Y 6 8 @