A particle moves along the y-axis with velocity given by v(t) = t sin(t^2) for t≥ 0.

a) In which direction (up or down) is the particle moving at time t = 1.5? Why?

b) Find the acceleration of the particle at time t = 1.5. Is the velocity of the particle increasing at t = 1.5? Why or why not?

c) Given that y(t) is the position of the particle at time t and that y(0) = 3, find y(2).

d) Find the total distance traveled by the particle from t = 0 to t = 2.</html