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 an answer does not exist, enter DNE.) f(t ) = 13 - 9+2+ 24t (a) Find the velocity (in ft/s) at time t. v (t ) = 312 - 181 + 24 it /s ( b ) What is the velocity ( in ft/s ) after 1 second ? ( 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.) (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 during the first 6 seconds. x it (f) Find the acceleration ( in ft/s2) at time t. a(t) = 6t - 18 At / s 2 Find the acceleration (in ft/s2) after 1 second. a (1 ) = -12 ft /s 2 (9) Graph the position, velocity, and acceleration functions for 0 S t s 6. 20 20 - 10 - 10 -10 -10 DO (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation. )