# Help with integrating the kinematic equations

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

Doc Al
Mentor
I am stuck on the second integration.

How do I integrate (t-to)dt from to --> t ??
How would you solve this?: ∫x dx

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

Doc Al
Mentor
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.)

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???

This is a really great website.
Indeed! :)

But does anyone have any ideas on how to type math symbols a little less akwardly than I'm doing???
You can use the LaTeX typesetting available on these forums. Check out this post: https://www.physicsforums.com/showthread.php?t=8997 for more details

Cool, I'll check that out for sure.

thanks!