A particle moves along the y-axis so that its position at any time is t> or equal to 0 is given by the

A particle moves along the y-axis so that its position at any time is t> or equal to 0 is given by y(t)=t^2 -4ln(t+1)-1

a. Find the velocity v(t) for any time t> or equal to 0.

b. For any time t> or equal to 0, find the lowest y value attained by the particle. Justify your answer.

c. Find all values of t for which the speed of the particle is increasing. Justify your answer.

d. Find the total distance traveled by the particle from time t=0 to time t=2.

Please help me out with this with explanations, I need to know how to do this kind of problem in case it comes on a test.

a. Find d/dt of y(t). [this is y']
b. Find for what value of t>=0 gives y'=0
c. Find d/dt of y'(t). [this is y''] and test where y'' is positive.
d. This will be the distance from y(t=0) to y(t = solution to part b), plus the distance from y(t = solution to part b) to y(t=2)

All explanations :)

lkjytdrgfh.