12. [4/10 Points] DETAILS PREVIOUS ANSWERS SCALCET9 3.7.001. MY NOTES A graphing calculator is recommended. A particle moves according to a law of motion s = ((t), t 2 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = +3 - 9t2 + 24t (a) Find the velocity (in ft/s) at time t. v(t) = 3t- - 18t + 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. Ift (f) Find the acceleration (in ft/s2) at time t. a(t) = ft/5 2 Find the acceleration (in ft/s2) after 1 second. a(1) = ft/52 (g) Graph the position, velocity, and acceleration functions for 0 s t = 6