A car of mass \(1600\text{ kg}\) passes through points \(A\) and \(B\) with speeds \(10\text{ m s}^{-1}\) and \(12\text{ m s}^{-1}\) respectively. The distance \(AB\) is \(2\text{ km}\). The heights of \(A\) and \(B\) above sea level are \(250\text{ m}\) and \(200\text{ m}\) respectively. The car’s engine does no work in moving from \(A\) to \(B\). There are two forces resisting the motion of the car, a braking force and an additional constant force of magnitude \(150\text{ N}\).

Use an energy method to find the work done by the braking force as the car moves from \(A\) to \(B\).