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Math Help - instantaneous velocity

  1. #1
    Senior Member euclid2's Avatar
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    instantaneous velocity

    a ball is thrown up in the air. it's height from the ground in meters after t seconds is modeled by h(t)=-5t^2+20t+1. what is the instantaneous velocity of the ball at t=2 seconds?

    i calculated h(2)=21 and h(2+h)=-5h^2+21 which i'm not sure are right

    what do i do from there?
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  2. #2
    Senior Member eumyang's Avatar
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    Have you learned derivatives yet? If so, then the derivative of h(t) would be
    h'(t) = -10t + 20
    and you can plug in t = 2.

    If not, have you learned limits? Then alternatively you could find
    \lim_{h \to 0} \dfrac{h(2 + h) - h(2)}{h}
    \lim_{h \to 0} \dfrac{-5h^2 + 21 - 21}{h}
    and take the limit. (Note that the h's are not the same, because I'm trying to be consistent with what you wrote.)
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  3. #3
    Senior Member euclid2's Avatar
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    i get -5h^2/h=-5(0)^2=0 so it is 0?
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  4. #4
    Senior Member eumyang's Avatar
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    Close.
    \lim_{h \to 0} \dfrac{-5h^2 + 21 - 21}{h} = \lim_{h \to 0} \dfrac{-5h^2 }{h} = \lim_{h \to 0} -5h = -5(0) = 0
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  5. #5
    Senior Member euclid2's Avatar
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    Does this mean that the instantaneous velocity at t=2 seconds is 0 m/s? It doesn't sound very "right to me"
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  6. #6
    Senior Member eumyang's Avatar
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    Quote Originally Posted by euclid2 View Post
    Does this mean that the instantaneous velocity at t=2 seconds is 0 m/s? It doesn't sound very "right to me"
    Sure it does. When you throw a ball up into the air, the velocity (I'm assuming that upwards is positive) will decrease. The ball slows down traveling upward, and it stops for an instant before traveling downward. So right before the ball falls back down, the velocity is 0 m/s.
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