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) = t3 - 7t2 + 20t (a) Find the velocity at time t. v(t) = 312 14t + 20 ft/s %3D - (b) What is the velocity after 1 second? v(1) = | 9 ft/s %D (c) When is the particle at rest? (d) When is the particle moving in the positive direction? (Enter your answer using interval notation.) (e) Find the total distance traveled during the first 6 seconds. ft