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 \left(\frac{\pi t}{2}\right) (a) Find the velocity (in ft/s) at time t. (b) What is the velocity (in ft/s) after 1 second? (c) When is the particle at rest? (Use the parameter n as necessary to represent any integer.) (d) When is the particle moving in the positive direction for 0 <= t<= 6? (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. (f) Find the acceleration (in ft/s²) at time t. Find the acceleration (in ft/s²) after 1 second. (g) Graph the position, velocity, and acceleration functions for 0 <= t <= 6. (h) When is the particle speeding up? (Enter your answer using interval notation.) When is it slowing down? (Enter your answer using interval notation.)