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

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 4.0 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 s, (g) 2.0 s, (h) 3.0 s, and (i) 4.0 s. Find its acceleration at times (j) 1.0 s, (k) 2.0 s, (l) 3.0 s, and (m) 4.0 s.