Serway & Jewett — Motion in One Dimension: Problem 33

Automotive engineers refer to the time rate of change of acceleration as the “jerk.” Assume an object moves in one dimension such that its jerk J is constant. (a) Determine expressions for its acceleration \(a_x(t)\), velocity \(v_x(t)\), and position \(x(t)\), given that its initial acceleration, velocity, and position are \(a_{xi}\), \(v_{xi}\), and \(x_i\), respectively. (b) Show that \(a_x^2 = a_{xi}^2 + 2J(v_x - v_{xi})\).