Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 22

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. What are the units of (a) constant c and (b) constant b? Let their numerical values be 3.0 and 2.0, respectively. (c) At what time does the particle reach its maximum positive x position? From \(t = 0.0\text{ s}\) to \(t = 4.0\text{ s}\), (d) what distance does the particle move and (e) what is its displacement? Find its velocity at times (f) \(1.0\text{ s}\), (g) \(2.0\text{ s}\), (h) \(3.0\text{ s}\), and (i) \(4.0\text{ s}\). Find its acceleration at times (j) \(1.0\text{ s}\), (k) \(2.0\text{ s}\), (l) \(3.0\text{ s}\), and (m) \(4.0\text{ s}\).