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 an answer does not exist, enter DNE.) f(t ) = ts - 9tz + 24t (a) Find the velocity (in ft/s) at time t. V (t ) = it/s (b) What is the velocity (in ft/s) after 1 second? V(1) = ft/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.) (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. = (1)E it/s 2 Find the acceleration (in ft/s ) after 1 second. a(1) = it/52(g) Graph the position, velocity, and acceleration functions for 0 s t s 6. 30- 20- 30 10 30 10- V 1 20 2 -10 4 6 10 O 1 2 -10 4 5 6 a 2 -10 4 5 6 a 30- AV 20 10 -10 4 (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.)