Halliday, Resnick & Walker — Motion Along a Straight Line: Problem 16

The position function \(x(t)\) of a particle moving along an \(x\) axis is \(x = 4.0 - 6.0t^2\), with \(x\) in meters and \(t\) in seconds. (a) At what time and (b) where does the particle (momentarily) stop? At what (c) negative time and (d) positive time does the particle pass through the origin? (e) Graph \(x\) versus \(t\) for the range \(-5\text{ s}\) to \(+5\text{ s}\). (f) To shift the curve rightward on the graph, should we include the term \(+20t\) or the term \(-20t\) in \(x(t)\)? (g) Does that inclusion increase or decrease the value of \(x\) at which the particle momentarily stops?