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Math Help - Instantaneous Velocity

  1. #1
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    Instantaneous Velocity

    A flare is shot up from the deck of a ship, the initial upward velocity of the flare is 30 m/s. The height of the flare is given by h=-5t^{2}+30t+10

    The Question is:
    Determine the instantaneous velocity of the flare at t=3 seconds by using the slopes of the secants.

    In other examples I found the instantaneous velocity by creating a table and using numbers that get closer and closer to 3 seconds until I can reach a conclusion.....but how do I use the slopes of the secants to find it?

    Thank you
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  2. #2
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    Quote Originally Posted by bearhug View Post
    A flare is shot up from the deck of a ship, the initial upward velocity of the flare is 30 m/s. The height of the flare is given by h=-5t^{2}+30t+10

    The Question is:
    Determine the instantaneous velocity of the flare at t=3 seconds by using the slopes of the secants.

    In other examples I found the instantaneous velocity by creating a table and using numbers that get closer and closer to 3 seconds until I can reach a conclusion.....but how do I use the slopes of the secants to find it?

    Thank you
    Ideally one would differentiate h and find the instantaneous velocity. Apparently "slope of secants" is the approximate idea of differentiation. So my guess is, "I found the instantaneous velocity by creating a table and using numbers that get closer and closer to 3 seconds until I can reach a conclusion" is called "slope of secants" method.

    Lets call the height h(t), since its a function of time, then instantaneous velocity at t=3 is \frac{h(3 + x) - h(3)}{x}, where x can be any small number(like 0.01,0.001 etc)
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  3. #3
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    Notice that \frac{h(3+x)- h(3)}{x} is the slope of the secant line: the line between (3, h(3)) and (3+x, h(3+x)). Do that calculation and see what happens for very small values of x.
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