Understanding Graphical Linearization: Exploring Linear and Non-Linear Graphs

[scorpa]

Hello everyone,

I am stuck on a problem relating to graphical linearization. The way we did it in high school was much easier than here. Anyway here is the question:

There are many ways to graph equation (1) d=Vot+(1/2)at^2, depending on the arrangement of the variables d vs t. However not all graphs are linear. Two different graphical arrangements in the form y vs x are:

(i) (t^2/d) vs (t/d)

(ii) (1/d) vs (t/d^2)

Solve equation (1) for the given y and then compare the rest of the expression to y=mx+b. Which graphs would be linear? Non-linear? In order to be linear, you must have variables and constants in the form y=slopex+intercept where (y,x) are variables and (slope, intercept) are constants. If the graph is linear, what quantities would correspond to the slope and intercept?

Ok, so that is the question. I think my biggest problem is that I do not understand what the question is asking me to do. If anyone could help me out with this I would really appreciate it, usually I at least have an idea of how to start a question but not this time unfortunately. Thanks a lot for any help you can give.

 

[hypermorphism]

For (i), it says "let y=(t^2)/d and let x=t/d and see if the equation (1) is algebraically equivalent to one of the form y=mx+b for some constants m and b."

 

[scorpa]

Yes, I understood that much but after that I was lost. Am I supposed to somehow plug those variables into the original equation? If so where do I plug them in, and by that I mean where do I substitute those given x and y values into the equation given. Thanks

 

[scorpa]

bump**********

 

[scorpa]

bumpity bump *cry* :P