Thursday, July 14, 2011

Calculus/physics help!?

If an object is dropped from an 80-meter high window, its height y above the ground at time t seconds is given by the formula y = f(t) = 80−4.9t2. (Here we are neglecting air resistance; the graph of this function was shown in figure 1.1.) Find the average velocity of the falling object between (a) 1 sec and 1.1 sec, (b) 1 sec and 1.01 sec, (c) 1 sec and 1.001 sec. Now use algebra to find a simple formula for the average velocity of the falling object between 1 sec and 1 + ∆t sec. Determine what happens to this average velocity as ∆t approaches 0. That is the instantaneous velocity at time t = 1 second (it will be negative, because the object is falling).

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