if im plotting a graph:
Time Squared vs Length
What will be the unit of my gradient ?
If time is on X axis and distance on Y axis then units will be m/sec^2.
what about time on y and length on x ?
That will be sec^2 per m but that is most unlikely to be required as generally time is taken as independent variable and variations are measured per unit time i.e. time rate of variation.
To determine the unit of the gradient when plotting Time Squared vs Length, we need to understand the units of each variable.
In this case, the x-axis represents Time Squared and the y-axis represents Length. Let's assume that time is measured in seconds (s) and length is measured in meters (m).
Now, let's calculate the unit of the gradient using the formula:
Gradient = (Change in y-axis value) / (Change in x-axis value)
In this case, the gradient represents the rate at which the length changes with respect to time squared. To find the unit of the gradient, we need to find the unit of Length per unit of Time Squared.
Unit of Gradient = (Unit of Length) / (Unit of Time Squared)
Since the unit of Length is meters (m) and the unit of Time Squared is seconds squared (s^2), the unit of the gradient will be:
Unit of Gradient = (m) / (s^2)
So, the unit of the gradient is meters per second squared (m/s^2). This unit represents the rate of change of length with respect to time squared in terms of meters per second squared.