Help with integrating the kinematic equations

  • Thread starter Markel
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  • #1
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Main Question or Discussion Point

Hello,

Just wondering if someone can help me make sense of something. I realize it's probably a simple problem, but my math skills aren't the best and I can't see through it.

I'm trying to end up with this kinematic equation:

X= Xo + Vo(t-to) + 1/2(a)(t-to)^2

And to do this the book tells me to insert this equation:
V=Vo + a(t-to)

Into this one:

X=Xo + ∫ vdt (integrated from to -> t)


And then solve this:

X=Xo + Vo∫ dt (from to->t) + a ∫ (t - to)dt (from to -> t)


I am stuck on the second integration.

How do I integrate (t-to)dt from to --> t ??

I realize that there are a few methods on how to get these equations, it seems like everybook I look at does it in a different way, but I want to understand this method.

(also, as you can probably tell, I'm new here and I'm not sure the best method of writing math symbols on a computer, can anyone sugest how to do it?)

thanks
 

Answers and Replies

  • #2
Doc Al
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I am stuck on the second integration.

How do I integrate (t-to)dt from to --> t ??
How would you solve this?: ∫x dx
 
  • #3
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How would you solve this?: ∫x dx
This would be 1/2[ X^2 - Xo^2]

And I know that's what I need to get for the kinematic equation but I don't see how.

If I have:

a∫(t-to)dt = a[ ∫ t dt -∫ to dt] <--- here I assume to is a constant

So integrating from to-->t give me:

a[ (t^2- to^2)/2 - to(t-to) ]

And this seems to lead to no where. arg.



Thanks for your quick reply
 
  • #4
Doc Al
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44,882
1,129
So integrating from to-->t give me:

a[ (t^2- to^2)/2 - to(t-to) ]
Expand that out and simplify. (Hint: Factor the resulting expression.)
 
  • #5
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ah, ok. Makes sense now. I was just making a mistake with the algebra and getting confused.

Thanks so much your speedy help, and your patience with me.
This is a really great website.

But does anyone have any ideas on how to type math symbols a little less akwardly than I'm doing???
 
  • #6
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  • #7
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Cool, I'll check that out for sure.

thanks!
 

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