The aerodynamic resistance to motion of a car is nearly proportional to the square of its velocity. Additional frictional resistance is constant, so that the acceleration of the car when coasting may be written in the following form: a = - C1 - C2v2, where C1 = 2.9 m/s2 and C2 = 0.00012 m-1 are constants which depend on the mechanical configuration of the car. Note: Acceleration is NOT a constant in this problem.

1) Using rectilinear motion equations, obtain a relationship between time t and velocity, v at that time.

2) Using the fact that acceleration is a function of velocity, and using rectilinear motion equations, obtain the relationship between distance traveled s and velocity, v at some arbitrary time, t.

3) If the car has an initial velocity v0 = 117 km/h when the engine is disengaged,

a) find the distance required for the car to come to a stop.

b) find the time taken for the car to come to a stop, if it starts at a time of 0 seconds.