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Homework Help: Instantaneous and average velocity help

  1. Sep 21, 2008 #1
    vAn objects moves horizontally according to the following equation s(t)=t3-2t2-5t+6. Determine the instantaneous velocity of the object at t0=1 second using the definition of a derivative at a point.

    v'(t)= lim (s(t0+h)-s(t0))/h
    h-->0


    And
    What is the average velocity of the object from t=0 to t=2?
    Average velocity= (s(t2)-s(t1))/(t2-t1)



    For the first one, i got:
    ((1+h)3-2(1+h)2-5(1+h)+6-13-2(1)2-5(1)+6)/h

    I expanded and factored all of that ang got (h(-1+h+h2)/h then i plugged in 0 for h and got -1 as the instantaneous velocity... is that correct?

    I got the first one... i just added the values wrong... i got -6. But i still dont know how to do the second one.

    and for the second one, i have (3(2)2-4(2)-5)/2-0 but that makes it 0/2 and i know that this cant be.

    Can you please help me?thank you!
     
    Last edited: Sep 21, 2008
  2. jcsd
  3. Sep 21, 2008 #2
    For the second part, it looks like you used the derivative of s (i.e. the velocity) in the numerator. You should use s itself (i.e. plug t1 and t2 into s(t) for the numerator) as in the definition of average velocity.
     
  4. Sep 21, 2008 #3
    so it should just be (-4-0)/(2-0)=-1/2?
     
  5. Sep 21, 2008 #4
    I think so. No. Wait a minute. Check it again. I think your t1 part is wrong. Just check it over carefully.
     
  6. Sep 21, 2008 #5
    wait wouldnt it be -5 for the average velocity instead?
     
  7. Sep 21, 2008 #6
    Yeah. That's what I get.
     
  8. Sep 21, 2008 #7
    thank you!!
     
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