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sha0403

a ball thrown straight up into the air so that its height in feet after t seconds is given by s(t)= 128t-16t^2.. so, find the average velocity of the ball during tie interval (2,2.1)

  • one year ago
  • one year ago

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  1. sauravshakya
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    can u find s'(t)

    • one year ago
  2. sha0403
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    yes.. after that i get 128-32t.. so what should i do that given time interval (2, 2.1)

    • one year ago
  3. sauravshakya
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    U need to find {s'(2) + s'(2.1)}/2

    • one year ago
  4. sha0403
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    why it divide by 2? can u explain to me?

    • one year ago
  5. sauravshakya
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    Because we are calculating avereage of two velocities

    • one year ago
  6. sha0403
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    oh like that..if we want to calculate average between 3 velocity,, we should divide by 3 also?

    • one year ago
  7. sauravshakya
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    yes

    • one year ago
  8. sauravshakya
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    add three valocities and dvide it by

    • one year ago
  9. sauravshakya
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    3*

    • one year ago
  10. sha0403
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    ok.... i would like to ask u something.. if the question ask to find instantaneous velocity at t=2.. what the mean of instantaneous/

    • one year ago
  11. sauravshakya
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    Just find s'(2)

    • one year ago
  12. sauravshakya
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    instantaneous means velocity of that body at that particular time

    • one year ago
  13. sauravshakya
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    got it?

    • one year ago
  14. wio
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    Umm, one thing I'd like to note is that @sauravshakya 's method for finding the average value works for lines. In this case velocity is indeed linear so it will work, though.

    • one year ago
  15. wio
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    Wait, actually @sauravshakya , the units don't seem to work out with your method. You have \(\frac{m/s}{s}\), which is acceleration.

    • one year ago
  16. wio
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    I think we don't need to do any calculus at all here. It's just: \[ \large \frac{s(t_f)-s(t_i)}{t_f-t_i} \]

    • one year ago
  17. sauravshakya
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    2 has no units

    • one year ago
  18. sauravshakya
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    I was just calculating average velocity

    • one year ago
  19. wio
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    Wow, that's right. I was wrong.

    • one year ago
  20. sha0403
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    @wio your formula when i should use it? what the kind of question?

    • one year ago
  21. wio
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    Anyway, I'm thinking that the average velocity, given velocity is: \[ \large \overline{v(t)} = \frac{1}{t_f-t_i}\int_{t_i}^{t_f} v(t) dt \]Note that \(s(t) = \int v(t) dt \), which gives us (by fundamental theorem of calc: \[ \frac{s(t_f) - s(t_i)}{t_f - t_i} \]

    • one year ago
  22. sha0403
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    @sauravshakya and @wio ..thank u very much

    • one year ago
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