The position of a particle moving along the x axis depends on the time according to the equation x = ct^2 − bt^3, where x is in meters and t in seconds. For the following, let the numerical values of c and b be 4.6 and 2.2, respectively.

(c) At what time does the particle reach its maximum positive x position?

(d) From t = 0.0 s to t = 4.0 s, what distance does the particle move?

(e) From t = 0.0 s to t = 4.0 s, what is its displacement?

(f) Find its velocity at t = 1.0 s.

(g) Find its velocity at t = 2.0 s.

(h) Find its velocity at t = 3.0 s.

(i) Find its velocity at t = 4.0 s.

(j) Find its acceleration at at t = 1.0 s.

(k) Find its acceleration at at t = 2.0 s.

(l) Find its acceleration at at t = 3.0 s.

(m) Find its acceleration at at t = 4.0 s.