Understanding Proportional Components in Equations

[physics-chris]

Homework Statement

Looking at a set of equations -how exactly do you work out if one component is proportional to another.

Homework Equations

In the example given s = ut + 1/2 at^2, I am told that s is not proporional to t unless acceleration is zero, because u is a constant.

The Attempt at a Solution

On one of my simpler questions, A=pi r^2, I am assumning that because pi is a constant A must be proportional to r^2 as that is what controlshow big or small A is.

On a second question v = u + at, I thought, as in the example that if acceleration is zero, that the final velocity must be proportional to time because u, the initial velocity, is a constant. But if acceleration is not zero then v is not proportional to t.

If that is correct, are there always (in most equations) some sort circumstances where the components that would be proportional in one circumstance, are not in another?

Thanks

 

[Doc Al]

In the example given s = ut + 1/2 at^2, I am told that s is not proporional to t unless acceleration is zero, because u is a constant.

For variable Y to be proportional to variable X just means that if X is increased by some factor, then Y is increased by the same factor. That's only true if the relationship between Y and X can be written like: Y = constant*X.

In this example, s = ut would be an example of proportionality, but s = ut + 1/2 at^2 would not.

The Attempt at a Solution

On one of my simpler questions, A=pi r^2, I am assumning that because pi is a constant A must be proportional to r^2 as that is what controlshow big or small A is.

Right. Here A is proportional to r^2, since A = constant*r^2. (Note that A is proportional to r^2, but not to r.)

 

[physics-chris]

Thanks- think I've sorted it now