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Problem 5. Suppose a car of mass m moving on a straight west-east highway at velocity v(t) (positive tor motion rom west to east experiences aerodynamic drag orce with magnitude αυ opposing its motion. The traction (force propelling the car forward by the ground) is equal to ku(t), where u(t) is the throttle angle (that determines the air/fuel flow into the engine). The parameters k, a are known positive constants. 1. Derive a dynamic model of the cars speed, relating the input u(t) to the output v(t) 2. Determine the transfer function from u to v. Is this transfer function BIBO stable? 3. Determine the transfer function from u to , where (t) is the position of the car at time t. Is this transfer function BIBO stable? 4. Is instability always bad or are there situations when it is desirable? (hint: think about the answer to the previous question)

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