# Proportionality in equations

1. Sep 27, 2009

### physics-chris

1. The problem statement, all variables and given/known data
Looking at a set of equations -how exactly do you work out if one component is proportional to another.

2. Relevant 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.

3. 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

2. Sep 27, 2009

### Staff: Mentor

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.

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.)

3. Sep 27, 2009

### physics-chris

Thanks- think i've sorted it now