A graphing calculator is recommended. A particle moves according to a law of motion s = f(t), t 2 0, where t is measured in seconds and s in feet. (If a f(t) = +3 - 9t2 + 24t (a) Find the velocity (in ft/s) at time t. v (t ) = 31 - 181 + 24 ft/s (b) What is the velocity (in ft/s) after 1 second? v(1 ) = 9 it/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.) t = (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (0,2) U (4,00) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled duri 44 ft (f) Find the acceleration (in ft/s2) at time t. a(t) = 6t - 18 ft/s2 Find the acceleration (in ft/s2) after 1 second. a(1) = -12 ft / s 2 (g) Graph the position, velocity, and acceleration functions for 0 S t s 6. 30 30 20 20 S 10- 10- 2 2 3- -10- -10 (h) When is the particle speeding up? (Enter your answer using interval notation.) X When is it slowing down? (Enter your answer using interval notation.) X