Suppose that a particle moves according to the law of motion 2t S = 12+ 5 ' t 2 0. (Round your answers to within three decimal places if necessary, but do not round until your final computation.) a. Find the velocity at time t. v( t) = b. What is the velocity after t = 3 seconds? v(3) = c. Find all values of t for which the particle is at rest. Enter enter DNE if the particle is never at rest. If there is more than one value, enter the values in a comma-separated list. t = seconds d. Determine when the particle is moving in the positive direction. Use interval notation, or enter DNE if no such intervals exist. Include the union symbol when entering multiple intervals. Interval of time: e. Find the total distance traveled during the first 8 seconds. Total distance