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Math Help - Instantaneous Velocity!

  1. #1
    Senior Member sakonpure6's Avatar
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    Instantaneous Velocity!

    How do you calculate it is? is it

    Velocity inst. = (df - di)/(tf - ti)

    or what??

    and instantaneous velocity is the average velocity between two points right?
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Instantaneous Velocity!

    Quote Originally Posted by sakonpure6 View Post
    How do you calculate it is? is it

    Velocity inst. = (df - di)/(tf - ti)

    or what??

    and instantaneous velocity is the average velocity between two points right?
    Not quite.

    Average velocity = (df - di)/(tf - ti)

    Instantaneous velocity is the velocity at one point.
    It is what you get if pick your ti and tf at the same time.
    You can't really do that since you'd be dividing by zero, but you can make the one approach the other as close as you want.
    This is what you do when you calculate a limit.
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  3. #3
    Senior Member sakonpure6's Avatar
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    Re: Instantaneous Velocity!

    Quote Originally Posted by ILikeSerena View Post
    Not quite.

    Average velocity = (df - di)/(tf - ti)

    Instantaneous velocity is the velocity at one point.
    It is what you get if pick your ti and tf at the same time.
    You can't really do that since you'd be dividing by zero, but you can make the one approach the other as close as you want.
    This is what you do when you calculate a limit.

    lets say i have those two points (1,20) and (2,40)

    would that make the instantaneous velocity 20 at 1.5?
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: Instantaneous Velocity!

    Quote Originally Posted by sakonpure6 View Post
    lets say i have those two points (1,20) and (2,40)

    would that make the instantaneous velocity 20 at 1.5?
    It would mean that you cannot find the instantaneous velocity without more information.

    Now if for instance your acceleration is zero, than your velocity will be the same everywhere.
    The instantaneous velocity would be the same as the average velocity then.
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  5. #5
    Senior Member sakonpure6's Avatar
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    Re: Instantaneous Velocity!

    well i have a set of data that makes up an increasing exponential function and i am supposed to find the acceleration of it and to do that my teacher said to take the instantaneous velocity between all two data points which would give me a linear function of where i can determine the acceleration by finding the slope.

    So i have the first two data points (0s , 0 cm [E]) and ( 0.05s, 0.80 cm [E]) , i determined that the instantaneous velocity between those points is 16 cm/s [E] at 0.025s. Is that right?
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  6. #6
    Super Member ILikeSerena's Avatar
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    Re: Instantaneous Velocity!

    What sort of set of data are you talking about?
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  7. #7
    Super Member ILikeSerena's Avatar
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    Re: Instantaneous Velocity!

    I think I understand.

    You have a set of data with a number of consecutive times, probably separated by 0.05 seconds.
    At each time you have a distance traveled in centimeters.

    Indeed, in that case the approximation of the instantaneous velocity is the average velocity between 2 consecutive points.
    This works because those 2 points are close enough together.
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  8. #8
    Senior Member sakonpure6's Avatar
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    Re: Instantaneous Velocity!

    so my answer of 16 is right?
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  9. #9
    Super Member ILikeSerena's Avatar
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    Re: Instantaneous Velocity!

    Quote Originally Posted by sakonpure6 View Post
    so my answer of 16 is right?
    Yes.
    Thanks from sakonpure6
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  10. #10
    Senior Member sakonpure6's Avatar
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    Re: Instantaneous Velocity!

    oh great! thank you very much!!!!!!!!!!!!!!!!
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