If a stone is dropped from a height of 400 feet, its height s after t seconds is given by s(t) = 400 – 16t2, with s in feet. (a) Compute s'(t). s'(t) = 32t Find the stone's velocity at times t = 0, 1, 2, 3, and 4 seconds. s'(0) = 0 v ft/sec s'(1) = 32 s'(2) = 64 s'(3) = 96 X ft/sec X ft/sec X ft/sec X ft/sec s'(4) = 128 (b) When does the stone reach the ground, and how fast is it traveling when it hits the ground? HINT [It reaches the ground when s(t) = 0.] The stone is traveling at a velocity of 160 x ft/sec when it hits the ground at 5 seconds.

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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.