At noon (t= 0), Alicia starts walking along a long, straight road at 4 mi/hr. Her velocity decreases according to the function v(t) = 4/(t + 1) for t2 0. At noon, Boris also starts walking along the same road with a 1-mi head start on Alicia; his velocity is given by u(t) = 2/(t + 1) for t20. %3D a. Find the position functions for Alicia and Boris, where s = 0 corresponds to Alicia's starting point. b. When, if ever, does Alicia overtake Boris? a. Alicia's position function is sA (t) = for t20.

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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.