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etotheipi

I appreciate that this is perhaps a strange question but it's been bugging me a little.

For instance, velocity is defined as the time derivative of position, so will always appear as the gradient a graph of x vs t. However, something like resistance as R = V/I is defined in terms of a ratio, and it would

Is there an easy way to tell which is true just by looking at the formula or must they just be learned? One rule I've sort of made up is that when the equation includes time in some form, e.g. Q = It, it is likely actually defined in terms of a derivative like dQ/dt, since we're dealing with a rate of change. All other equations I can think of that don't include time seem to be defined with ratios, for instance things like V=IR, M=pV, F=PA etc.

This seems to work pretty well, but I don't want to learn something wrong that might cause confusion in the future. Can you think of any exceptions to this?

I just remembered dW/dx = F as a counter example, for instance if we plotted the cumulative work done as a function of displacement. Evidently my rule is a bit wrong.

For instance, velocity is defined as the time derivative of position, so will always appear as the gradient a graph of x vs t. However, something like resistance as R = V/I is defined in terms of a ratio, and it would

**not**be correct to interpret it as the gradient unless in the special case where current happens to be constant. Instead, we would determine R graphically by reading off values.Is there an easy way to tell which is true just by looking at the formula or must they just be learned? One rule I've sort of made up is that when the equation includes time in some form, e.g. Q = It, it is likely actually defined in terms of a derivative like dQ/dt, since we're dealing with a rate of change. All other equations I can think of that don't include time seem to be defined with ratios, for instance things like V=IR, M=pV, F=PA etc.

This seems to work pretty well, but I don't want to learn something wrong that might cause confusion in the future. Can you think of any exceptions to this?

**Edit**I just remembered dW/dx = F as a counter example, for instance if we plotted the cumulative work done as a function of displacement. Evidently my rule is a bit wrong.

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