A motorized cart of mass \(m\) is placed on a straight, horizontal track. The cart's onboard computer is programmed to follow a specific velocity-time profile. Let \(x = 0\) be the cart's initial position at \(t = 0\). A graph of the cart's velocity \(v\) as a function of time \(t\) is shown below, where \(v_0\) and \(t_0\) are positive constants.