When to use gradient and when to use only one coordinate

[FaroukYasser]

Hi,
I was wandering, sometimes in physics, to get acceleration from a velocity time graph, you would have to find the gradient of the tangent of the curve. But in other graphs like say Voltage current graph, if you want to find the resistance at any point (Which is V/I) you simply take the coordinate of that point and just divide Voltage by Current. Why is it that we took there the gradient of a tangent and here just the coordinates although in both the Gradient represented acceleration and Resistance.

Thanks

 

[dauto]

That depends on the definition of the physical quantity you're trying to calculate. resistance is defined as R =V/I while acceleration is defined as a=Δv/Δt.

 

[Chestermiller]

Hi,
I was wandering, sometimes in physics, to get acceleration from a velocity time graph, you would have to find the gradient of the tangent of the curve. But in other graphs like say Voltage current graph, if you want to find the resistance at any point (Which is V/I) you simply take the coordinate of that point and just divide Voltage by Current. Why is it that we took there the gradient of a tangent and here just the coordinates although in both the Gradient represented acceleration and Resistance.

Thanks

In the case of voltage, resistance, and current, you don't divide the voltage by the current, you divided the voltage difference across the resistor by the current. The voltage difference across the resistor is equal to the voltage gradient times the length of the resistor. The resistance divided by the length of the resistor is equal to the resistivity times the cross sectional area. So the resistivity is equal to the voltage gradient divided by the current density.

chet