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)
Find the time it takes for the speed to drop to 0.001 m/sec (or 1
Find the initial braking force at t = 0.
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