A particle moves along the x-axis so that its velocity is given by

v(t)= -(t+1)sin(t^2/2)

****at time t=0, the particle is at position x=1

a) Find the acceleation of the particle at time t=2. Is the speed of the particle increasing at t=2? Why or Why not?

b) Find all times t in the open interval 0,t,3 when the particle changes direction.Justify your answer.

c)Find the total distance traveled by the particle from time t=0 until time t=3

d) During the time interval 0<=t<=3, , what is the greatest distance between the particle and the origin?

I WOULD GREATLY APPRECIATE IT IF SOMEONE WOULD HELP ME OUT ON THIS PROBLEM AND GIVE ME THE CORRECT ANSWERS SO I CAN SEE IF MINE ARE CORRECT. I'M DESPERATE , PLEASE HELP.

- ALLEN