Help with integrating the kinematic equations

In summary, the conversation is about understanding a kinematic equation and how to solve it using integration. The person is having trouble with the second integration and asks for help. They also mention being new to the forum and ask for suggestions on typing math symbols. Another user suggests using LaTeX typesetting available on the forum.
  • #1
Markel
84
0
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
 
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  • #2
Markel said:
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
Doc Al said:
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
Markel said:
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
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
Markel said:
This is a really great website.
Indeed! :)

Markel said:
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
 
  • #7
Cool, I'll check that out for sure.

thanks!
 

What are the kinematic equations?

The kinematic equations are a set of mathematical equations that describe the relationship between an object's position, velocity, acceleration, and time. They are used to analyze and predict the motion of objects.

How do I use the kinematic equations?

To use the kinematic equations, you must first identify the known values for an object's position, velocity, acceleration, and time. Then, plug these values into the appropriate equation and solve for the unknown quantity.

What is the difference between the five kinematic equations?

Each of the five kinematic equations represents a different aspect of an object's motion. The first three equations relate to an object's displacement, velocity, and acceleration when the initial velocity is known. The last two equations involve an object's displacement and velocity when acceleration is constant.

Can I use the kinematic equations for any type of motion?

The kinematic equations are most accurate for objects moving in a straight line with constant acceleration. They can also be used for objects moving in a curved path, but the calculations may be less precise.

Are there any limitations to the kinematic equations?

Yes, the kinematic equations assume that there is no external force acting on the object and that the acceleration is constant. They also do not take into account factors such as air resistance or friction, which can impact an object's motion in the real world.

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