Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities haveunits of m/s complete parts through A a. Determine when the motion is in the positive direction and when it is in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. v(t)=3 t^{2}-36 t+105 ;[0,8] a. When is the motion in the positive direction? Select the correct choice below and, if necessary, fill in the answer box(es)to complete your choice. OA. For t-values that satisfy B. The motion is never in the positive direction. When is the motion in the negative direction? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. For t-values that satisfy B. The motion is never in the negative direction. b. The displacement of the particle is c. The total distance traveled by the particle is