Question

Determine when motion is positive and negative for v(t)=5sin(1/2t) on [0,6pi]

Answer 1

I think you mean: "Determine when motion is in the positive direction and when it is in the negative direction for v(t)=5sin(1/2t) on [0,6pi]." Simply seet v(t) = 0 and determine where v(t) = 0. The resulting roots will be the end points of subintervals on the positive number line. Determine on which intervals v(t) is (+) and on which it is (-).