It is a consequence of Newton's law of gravitation that near the surface of any planet, the distance D fallen by a rock in time t is given by D = ct2. That is, distance fallen is proportional to the square of the time, no matter what planet one may be on. But the value of c depends on the mass of the planet. For Earth, if time is measured in seconds and distance in feet, the value of c is 16. (a) Suppose a rock is falling near the surface of a planet. What is the comparison in distance fallen from 3 seconds to 12 seconds into the drop? (Hint: This question may be rephrased as follows: "If time increases by a factor of 4, by what factor will distance increase?")

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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.