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Calculus Average Velocity

  1. Oct 10, 2011 #1
    1. The problem statement, all variables and given/known data

    A ball is thrown into the air a velocity of 49 ft/s. Its height in feet after t seconds is given by y=49t-10t^2.

    A. Find the average velocity for the time period beginning when t=3 and lasting
    0.01 s:
    0.005 s:

    B. Estimate the instantaneous velocity when t=3.


    2. Relevant equations

    Integrals

    3. The attempt at a solution

    I'm not exactly sure if I'm approaching this problem at the right angle...

    A) 0.01s

    1/ [(3.01) -3] ∫ from 3 to 3.01 49t-10t^2 dx

    [1/0.01] ∫ from 3 to 3.01 49t-10t^2 dx

    [1/0.01] ∫ from 3 to 3.01 (49t^2)/2 - (10t^3)/3 <------ integrated

    [1/0.01] [(49(3.01)^2)/2 - (10(3.01)^3)/3] - [1/0.01] [ 49(3)^2)/2 - (10(3)^3)/3

    substitution

    Same steps for 0.005s

    B) I'm not sure how to approach this problem.

    Please help me understand the problem. Thank you very much. :)
     
  2. jcsd
  3. Oct 10, 2011 #2

    eumyang

    User Avatar
    Homework Helper

    No, you don't want to take an integral. You're given a position function, and integrating it doesn't give you the velocity function. What you want to do is to use the average rate of change formula (from x = a to x = b):
    [tex]\frac{f(b) - f(a)}{b - a}[/tex]
    So, given the position function s(t) = -10t2 + 49t, evaluate
    [tex]\frac{s(3.01) - s(3)}{3.01 - 3}[/tex]

    Do you know the formula for finding a derivative at a point (I'm talking about the one with the limit)?
     
  4. Oct 10, 2011 #3
    Actually, I don't know the formula for finding a derivative at a point.
     
  5. Oct 10, 2011 #4

    eumyang

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    Homework Helper

    Sure you do:
    [tex]f'(a) = \lim_{h \rightarrow 0} \frac{f(a + h) - f(a)}{h}[/tex]
     
  6. Oct 10, 2011 #5
    Thanks. :D
     
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