Variable Relationships in Kinematics

[rocketbooster]

Advertisement - Members don't see this ad

The kinematic equations are...

v=v0+at
v^2=v0^2 + 2ad
d=v0t + 0.5at^2

what are the relationships between d and t, v and t, v and d, v and a, d and a, and so forth?

It's good to know because sometimes graphs comparing 2 of the kinematics relationships comes up.

I just get confused sometimes because looking at a different kinematics equation seems to give you a different relationship.

For example, look at v and a. Equation 1 says v and a are directly proportional while equation 2 says v^2 and a are proportional. Which one is it? How do you know which equation to use to find the correct relationship?

 

[ksmi117]

You need four of the components to have a relationship. If I gave you v and a, you can't know v0, d, or t without one of the others.

These graphs, do they like give you v0 and a and then have a graph of d vs. t? Because other than that, they really don't make much sense to me. Can you give an example? Obviously, you can't draw the graph, but explain the context when you'd find one of the graphs.

All in all, the relationship depends on which of the other components are invovled. In equation 1, a seems proportional to v because it also involves v0 and t. In equation 3, a seems proportional to v^2 because it also involves d and t.

 

[rocketbooster]

You need four of the components to have a relationship. If I gave you v and a, you can't know v0, d, or t without one of the others.

These graphs, do they like give you v0 and a and then have a graph of d vs. t? Because other than that, they really don't make much sense to me. Can you give an example? Obviously, you can't draw the graph, but explain the context when you'd find one of the graphs.

All in all, the relationship depends on which of the other components are invovled. In equation 1, a seems proportional to v because it also involves v0 and t. In equation 2, a seems proportional to v^2 because it also involves d and t.

ohhh, so the relationships are never consistent from problem to problem. they are only consistent within that ONE problem.

I don't remember an exact example, but like...I think it'll say to hold everything else constant and then ask for the relationship between the 2 changing variables. in that case, which equation do you use?

it'll usually be a passage on kinematics...and then like the last equation will ask for the graph of the relationship between 2 variables. when you look at the answer in the back, sometimes they base it on equation 1 and other times they base it on equation 2. I don't know. 🙁

 

[ksmi117]

ohhh, so the relationships are never consistent from problem to problem. they are only consistent within that ONE problem.

I don't remember an exact example, but like...I think it'll say to hold everything else constant and then ask for the relationship. in that case, which equation do you use?

It depends on what is given. If they give you v0 and a, and ask for v vs. t, use 1. If they give v0 and a, and ask for d vs. t, use 3. etc...

 

[rocketbooster]

It depends on what is given. If they give you v0 and a, and ask for v vs. t, use 1. If they give v0 and a, and ask for d vs. t, use 3. etc...

ohh, okay, yea that makes sense. and for the bolded part, you wouldn't use equation 2, even tho you have all the variables, because the t and t^2 values in one equation do not give a clear relationship, right?

 

[rocketbooster]

okay, yea. makes perfect sense. not sure why i was confused

 

[EgyptianDoc]

Rocket,

There is actually a way to derive and compare d vs. t, v vs. t, and a vs. t graphs. Is this what you're asking about? It's in my notes. Sometime tonight or tomorrow I will scan it and explain how it works! 🙂

 

[Bernoull]

Rocket,

There is actually a way to derive and compare d vs. t, v vs. t, and a vs. t graphs. Is this what you're asking about? It's in my notes. Sometime tonight or tomorrow I will scan it and explain how it works! 🙂

just to second this. If you know calculus it's very clear what the relationships between these variables are. They are all functions of time, and the easiest derivation will be to start from a=dv/dt. Check this link out.

http://webphysics.iupui.edu/152/152Basics/kinematics/kinderive.html

 

[EgyptianDoc]

Not sure if this is exactly what you're asking. The document is attached. Basically, you break the graphs into components, which makes deriving the other 2 graphs really easy. Let me know if you need further explaining but it's pretty self-explanatory. I learned this is a PR course in case you were wondering.