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1. A test model for a new type of braking system is designed to apply a braking force that decays following an exponential function. For an object moving in the (+) X direction (to the right), the force acts in the opposite direction. When the brakes are applied, the velocity change as a function of time in seconds can be approximated by = where Vo is a constant in [m/sec] and A is a constant in [1/sec]. a) Find an equation for the acceleration and the force applied by the brakes as a function of time. Use m for the mass of the object. Are the force and acceleration constants? (12 pts) b) Find an equation for the distance travelled as the moving object comes to a stop. At the initial point where the brakes are activated, take time t = 0 and position Xo = 0. (12 pts) c) In the test model, the brakes are activated at an initial speed of 5 m/sec. The unit has a mass of 2 kg. The system is set so that A = 2 1/sec. (6 pts) i. Find the time it takes for the speed to drop to 0.001 m/sec (or 1 mm/sec). ii. Find the initial braking force at t = 0.

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