When the driver of a vehicle observes an impediment, the total stopping distance involves both the reaction distance (the distance the vehicle travels while the driver moves his or her foot to the brake pedal) and thebraking distance (the distance the vehicle travels once the brakes are applied). For a car traveling at a speed of v miles per hour, the reaction distance R, in feet, can be estimated by R(v) = 2.2v. Suppose that the braking distance B, in feet, for a car is given by B(v) = 0.05v2 + 0.4v - 15.(a) Find the stopping distance function D(v) = R(v) + B(v). (b) Find the stopping distance if the car is traveling at a speed of 60 mph.(c) Interpret D(60).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.