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Instanteous velocity 
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#1
Sep408, 07:47 PM

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1. The problem statement, all variables and given/known data
If an arrow is shot upward on the moon with a velocity of 59 m / s, its height in meters after t seconds is given by h = 59(t)  .83(t)². Find the instantaneous velocity after one second. 2. Relevant equations 3. The attempt at a solution h = 59(1)  .83(1)^{2} h = 58.17 h = 59(1.0000001) .83(1.0000001)^{2} h = 59.0000059  0.8300001660000083 h = 58.1700057339999917 v = 58.1700057339999917  58.17 / .0000001 v = 57.339999917 thats as far as i get. i think the instant vel would be 57.3 m / s because it wont take the answer 57 or 57.5. can someone help me? 


#2
Sep408, 07:53 PM

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Since you've posted this in the calculus forums, I'm guessing that we should use calculus. So, what is the definition of instantaneous velocity, or velocity in general? 


#3
Sep408, 07:56 PM

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The speed at which an object is moving at any given time. right?



#4
Sep408, 08:02 PM

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Instanteous velocity



#5
Sep408, 08:05 PM

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v =[tex]\Delta[/tex]d/[tex]\Delta[/tex]t



#6
Sep408, 08:09 PM

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[tex]v=\lim_{t\to0}\frac{\Delta h}{\Delta t} = \frac{dh}{dt}[/tex] Do you follow? 


#7
Sep408, 08:11 PM

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Yes, so far.



#8
Sep408, 08:13 PM

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#9
Sep408, 08:21 PM

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h'(t) meaning the inverse?



#10
Sep408, 08:30 PM

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h'(t) meaning the first derivative of h with respect to t. As I said in my previous post, velocity is defined as the rate of change of displacement with time. 


#11
Sep408, 08:35 PM

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#12
Sep408, 08:43 PM

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[tex]\frac{dh}{dt} = \frac{d}{dt}\left(59t  0.83t^2\right)[/tex] Does that make sense? 


#13
Sep408, 08:50 PM

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Yes, that makes alot more sense.
so, basically. I need to plug in the change in height for dh and change in time for dt. then solve? im still not sure what d by itself it. 


#14
Sep408, 08:52 PM

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#15
Sep408, 08:56 PM

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Yes, but I'm really lost.
How would I find the derivative? 


#16
Sep408, 08:59 PM

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#17
Sep408, 10:03 PM

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After studying the chapter and doing some research in my calculus book, I have calculated that the velocity at 1 second is 57.34 m / s.
Does this sound right to you? 


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