Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 5

5 The position of an object moving along an x axis is given by \(x = 3t - 4t^2 + t^3\), where \(x\) is in meters and \(t\) in seconds. Find the position of the object at the following values of \(t\): (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s. (e) What is the object’s displacement between \(t = 0\) and \(t = 4\) s? (f) What is its average velocity for the time interval from \(t = 2\) s to \(t = 4\) s? (g) Graph \(x\) versus \(t\) for \(0 \leq t \leq 4\) s and indicate how the answer for (f) can be found on the graph.