A car rolling on a hill can be modeled as shown in Figure E-25. The excitation is the force for which a positive value represents accelerating the car forward with the motor and a negative value represents slowing the car by braking action. As it rolls, the car experiences drag due to various frictional phenomena that can be approximately modeled by a coefficient which multiplies the car’s velocity to produce a force which tends to slow the car when it moves in either direction. The mass of the car is m and gravity acts on it at all times tending to make it roll down the hill in the absence of other forces. Let the mass m of the car be 1000 kg, let the friction coefficient be 5 N •s/m and let the angle 0 be ?/12.
and the position of the car y(t) as the response.
(b) If the nose of the car is initially at position y(0) = 0 with an initial velocity 
and no applied acceleration or braking force, graph the velocity of the car y’(t) for positive time.
(c) If a constant force f(t) of 200 N is applied to the car what is its terminal velocity ?
Solution:
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