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Thread: Average Velocity

  1. #1

    Average Velocity

    Again, I'm sure this doesn't go here but it's a problem I got in my Calculus class, so I'm posting it here.

    I have the following question:
    If a ball is thrown in the air with a velocity 34 ft/s, its height in feet t seconds later is given by y = 34t − 16t2.
    (a) Find the average velocity for the time period beginning when t = 2 and lasting

    With the following answers:
    (i) 0.5 second.
    38 ft/s

    (ii) 0.1 second.
    31.6 ft/s

    (iii) 0.05 second.
    30.8 ft/s

    (iv) 0.01 second.
    30.16 ft/s

    (b) Estimate the instantaneous velocity when t = 2.
    30 ft

    But they're all wrong. Here's how I worked it out:
    Avg Velocity= (change in)y/(change in) x= y (2+ h)- y (2)/(2+h) - 2
    Then, I worked all that through and got = -16h -30
    I plugged the value of h in each time.
    AV= -16 (.5)-30= -38ft/sec
    AV= -16 (.1) - 30= 31.6 ft/sec
    etc, etc.

    Can negative numbers work with this? Do I need to just change the signs? Or did I screw up bad somewhere in the math? Also, is there an easier way to figure this out?
    I can only submit this one more time, so I need to make SURE I have the right answer this time.

  2. #2
    The example I watched had the following:
    If a ball is thrown into the air with a velocity of 40 ft/s, its height in feet t seconds later is given by y= 40t - 16t^2.

    Find the average velocity for the time period beginning when t=2 and lasting

    i) 0.5 seconds

    First she used a formula for average velocity.
    t=2 to t= 2 + h
    (change in)y/(change in)t = y (2 + h)- y(2)/ (2+h) - (2)

    = 40 (2+ h) - 16 (2 + h)^2 - [40 (2)- 16 (2)^2] / h
    =80 + 40h - 16 (4 + h^2 + 4h) - 80 + 64/ h
    = 40h- 64-16h^2-64h +64 / h
    =-16h^2 - 24h/ n
    = h (-16h - 24)/ h
    = -16h - 24

    Next she plugs in the values.
    h= .5
    A.V.= -16 (.5) - 24= -32ft/s

    &so on and so on.

    But this was the example I was given from the text for our class.

  3. #3
    Thanks! Your way seems much more simple.
    So, should the answer for 0.1 be 32.4?
    See this threw me off because I saw the velocity was going from 34, to 26, to 32.4?

    Then, for 0.05= 33.2?

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