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A graphing calculator is recommended. A particle moves according to a law of motion s = f(t), t≥ 0, where t is measured in seconds and s in feet. (If an answer does not exist, enter DNE.) f(t) = sin (a) Find the velocity (in ft/s) at time t. v(t) = t = лt (b) What is the velocity (in ft/s) after 1 second? v(1) = ft/s (c) When is the particle at rest? (Use the parameter n as necessary to represent any integer.) ft/s (d) When is the particle moving in the positive direction for 0 ≤ t ≤ 6? (Enter your answer using interval notation.) a(t) = (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/s²) at time t. ft/s² a(1) = Find the acceleration (in ft/s²) after 1 second. ft/s² (g) Graph the position, velocity, and acceleration functions for 0 ≤ts 6. k
(g) Graph the position, velocity, and acceleration functions for 0 ≤ t ≤ 6. V a ע a /3 t i (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.) V S 1 a 5 V S ba a