A \(2.2 \mathrm{~kg}\) measuring instrument is mounted on a balloon by your scientific team for atmospheric studies. At the top of its flight, the instrument is released from the balloon and falls most of the way back to Earth before a parachute opens. You are told that the magnitude of the acceleration at any instant \(t\) before the parachute opens is given by \(|a|=g e^{-t / \tau}\), where \(g\) is the acceleration due to gravity, \(c\) is the base of natural logarithms, and \(\tau\) is a time constant that depends on the shape of the instrument and in this case is \(5.68 \mathrm{~s}\). Your primary concern is how much the instrument heats up as it falls, due to air resistance. At what rate, in joules per second, is energy dissipated before the parachute opens? Express your answer as a function of \(t\), where \(t=0\) at release. (Integrate the acceleration to calculate speed and displacement.)