A particle moves according to a law of motion s = At), t 2 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) At) - t - 9+2 + 24t (a) Find the velocity (in ft/s) at time t. "(t) - 37- - 181 + 24 - ft/s (b) What is the velocity (in ft/s) after 1 second? v(1) - 9 ft/s (c) When is the particle at rest? (Enter your answers as a comma-separated list.) t - 2,4 (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Draw a diagram to illustrate the motion of the particle and use it to find the total distance (in ft) traveled during the first 6 seconds. ft (f) Find the acceleration (in ft/s?) at time t. At/s 2 Find the acceleration (in ft/s ) after 1 second. a(1) = ft /s 2 (g) Graph the position, velocity, and acceleration functions for 0 s t s 6. 30 20 20 10 -10 -10 30 30 20 20V 10 10 -10 -10 A (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.)