The velocity (in mi/hr) of an airplaneflying into a headwind is given by v(t) = 30(16 - t2),for 0 ≤ t ≤ 3. Assume s(0)= 0 and t is measured in hours.a. Determine the position function, for 0 ≤ t ≤ 3.b. How far does the airplane travel in the first 2 hr?c. How far has the airplane traveled at the instant its velocityreaches 400 mi/hr?

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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.