This problem has to do with the motion of a car along a straight road. The mass of the car is m, its drag resistance is C_d, the rolling resistance of the tires is μ_r. Choose any car that you'd like to analyze and obtain its data (cite your source). Look up typical values of rolling resistance. For the MATLAB portions, explore these questions for different values of mass of the car (which would depend on the number of passengers and luggage in the car) and the rolling resistance (which would depend on the inflation pressure of the tires)
(a) Determine the differential equation if the car is traveling along a flat road.
(b) Determine the traction force corresponding to speed v_e.
(c) (MATLAB) Determine the 0-60 mph time and distance.
(d) (MATLAB) Determine the velocity and distance as a function of time if the car is to be started from rest and is supplied with the tractive force for 30 mph.
(e) (MATLAB) If the car is travelling at a steady speed 30 mph and it's to be sped up to 60 mph,
determine velocity and distance as a function of time.
(f) (MATLAB) If the car is travelling at 60 mph and it's to be slowed down to 30 mph, determine
the velocity and distance as a function of time.
(g) (MATLAB) If the car is travelling at 60 mph and it's to be brought to rest, determine the velocity and distance as a function of time. Determine the time it takes to bring the car to rest.

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