Slowest shortcut Suppose you are standing in a field near astraight section of railroad tracks just as the locomotive of a trainpasses the point nearest to you, which is 1/4 mi away. The train,with length 1/3 mi, is traveling at 20 mi/hr. If you start runningin a straight line across the field, how slowly can you run and stillcatch the train? In which direction should you run?

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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.