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math456

  • 3 years ago

If a ball is thrown into the air with a v of 40 ft/s, it's height in ft t seconds late is given by y= 40t-16t^2. Find the avg velocity for the time period beginning when t=2 & lasting 0.5 sec, 0.05 sec?

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  1. Algebraic!
    • 3 years ago
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    so the distance covered / the time interval is what you're looking for...

  2. Algebraic!
    • 3 years ago
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    do you know how to find the distance covered between t=2 and t=2.5?

  3. math456
    • 3 years ago
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    The average velocity!

  4. math456
    • 3 years ago
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    Yea it's like u plug in the 2 in the equation and then distance covered in 2-distance coverd in 2.5/2-2.5

  5. Algebraic!
    • 3 years ago
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    yes

  6. math456
    • 3 years ago
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    So in this case is .5 sec= 0?

  7. Algebraic!
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    no.

  8. math456
    • 3 years ago
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    And 0.05=7.2

  9. Algebraic!
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    find y(2) find y(2.5)

  10. Algebraic!
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    then find the difference between those two heights

  11. Algebraic!
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    then divide by the time interval (.5s)

  12. math456
    • 3 years ago
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    But 2.5 is not in the question..

  13. Algebraic!
    • 3 years ago
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    k

  14. Algebraic!
    • 3 years ago
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    2 + .5 = ?

  15. math456
    • 3 years ago
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    2.5 ohh gotch ya so all I do is divide by the 0.5, 0.05?

  16. math456
    • 3 years ago
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    So for 0.5 it's 32?

  17. Algebraic!
    • 3 years ago
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    let me check

  18. math456
    • 3 years ago
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    Okay

  19. Algebraic!
    • 3 years ago
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    yep

  20. math456
    • 3 years ago
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    And for 0.05 is 320?

  21. Algebraic!
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    don't think so... how'd you get that

  22. math456
    • 3 years ago
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    Y(2)-y(2.5)/0.05

  23. Algebraic!
    • 3 years ago
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    naw...

  24. Algebraic!
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    y(2) and y(2.05)

  25. math456
    • 3 years ago
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    U r adding the values to 2.0?

  26. Algebraic!
    • 3 years ago
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    height at 2 seconds and height .05 seconds later ( y(2.05) )

  27. math456
    • 3 years ago
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    so for 0.01 second its y(2)-y(2.01)

  28. Algebraic!
    • 3 years ago
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    \[(d _{f} - d _{i})/(t _{f} -t _{i})\]

  29. Algebraic!
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    yep

  30. math456
    • 3 years ago
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    okay how abt if i want to find the estimate instantaneous velocity when t=2

  31. math456
    • 3 years ago
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    sorry t=1*

  32. Algebraic!
    • 3 years ago
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    if you're allowed to use calculus you just take the derivative...

  33. Algebraic!
    • 3 years ago
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    if not, you take the limit of the avg. velocity expression as t->0

  34. math456
    • 3 years ago
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    ummm not sure what u meant so when t=2 its t>0

  35. Algebraic!
    • 3 years ago
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    the third alternative is using the equation that you might've been given where the derivative is already taken for you...

  36. Algebraic!
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    something like \[V(t) = V _{o} +at\]

  37. Algebraic!
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    seen that before?

  38. math456
    • 3 years ago
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    can i just do like 32-14.76M0.5-0.05N

  39. math456
    • 3 years ago
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    yea i hv seen it

  40. math456
    • 3 years ago
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    sorry here m is the divide sign

  41. Algebraic!
    • 3 years ago
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    The three ways I mentioned are the ways to do it, not sure what you typed there or what you're trying to do.

  42. Algebraic!
    • 3 years ago
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    You all good on this? Or do you have another question?

  43. math456
    • 3 years ago
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    how how can i take the limit of avg. velocity at t>0?

  44. math456
    • 3 years ago
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    @Algebraic!

  45. Algebraic!
    • 3 years ago
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    like:

  46. Algebraic!
    • 3 years ago
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    for a specific value of t?

  47. math456
    • 3 years ago
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    t=2

  48. Algebraic!
    • 3 years ago
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    I'll use the sketch pad to show you

  49. math456
    • 3 years ago
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    okay, thanks

  50. Algebraic!
    • 3 years ago
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    |dw:1347077529182:dw|

  51. Algebraic!
    • 3 years ago
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    that's the first term...

  52. math456
    • 3 years ago
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    hmmm how do I find the delta t value?

  53. Algebraic!
    • 3 years ago
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    |dw:1347077587650:dw|

  54. Algebraic!
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    that's the second term

  55. math456
    • 3 years ago
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    okay.

  56. Algebraic!
    • 3 years ago
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    all that gets divided by delta t

  57. Algebraic!
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    then you take the limit as delta t ->0

  58. math456
    • 3 years ago
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    so the limit as x approaches to 0 is -16

  59. math456
    • 3 years ago
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    for inst. velocity?

  60. Algebraic!
    • 3 years ago
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    should be -24

  61. math456
    • 3 years ago
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    let me check again..

  62. math456
    • 3 years ago
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    okay got it nw..

  63. Algebraic!
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    cool;)

  64. math456
    • 3 years ago
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    thanks for ur help..

  65. Algebraic!
    • 3 years ago
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    No problem!

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