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**macroecon** 1) A particle moves along the x-axis so that, at any time t≥0, its acceleration is given by a(t)=6t-3. At time t=0, the velocity of the particle is -18, and its position is -27.

a) Find v(t), the velocity of the particle at any time t≥0.

b) For what values of t≥0 is the particle moving to the right?

c) Find x(t), the position of the particle at any time t≥0.

2) Let y=2e^(sinx)

a) Calculate dy/dx (1st derivative) and d2y/dx2 (2nd derivative).

b) If x and y both vary with time in such a way that y increased at a steady rate of 5 units per second, at what rate is x changing when x=pi?

Any help would be appreciated, even if you just explain to me the steps or methods I should be using.