For 0 ≤ t ≤ 8 , a particle moving in the xy-plane has position vector 〈x(t),y(t)〉=〈sin(2t),t^2−t〉 , where x(t) and y(t) are measured in meters and t is measured in seconds. Find the speed of the particle at time 1 = 2 seconds. Indicate units of measure. (b) At time t = 4 seconds, is the speed of the particle increasing or decreasing? Explain your answer. (c) Find the total distance the particle travels over the time interval 0 St S5 seconds. (d) At time t = 8 seconds, the particle begins moving in a straight line. For t≥8, the particle travels with the same velocity vector that it had at time t = 8 seconds. Find the position of the particle at time t = 10 seconds.