Significance of Gradient

[kenhung123]

What is the significance of gradient for several measured variables? How do we identify the 'significance'?

[/0]

Whenever you have any relation , where A and B are measured variables, then obviously the gradient will give you k. The advantage of the gradient is it contains the information of all the data points, so it's better than using any one data point to find k.

[rashmi_34]

In addition to what /0 has said;
the gradient with respect to B will tell you how much variable A will change for every unit of B.

eg) v=at+u, with respect to "t" the gradient is "a"(acceleration). Here, "a" is the amount which v(velocity) changes when u wait for one unit of t(time in sec)
      v=5t+2, therefore gradient=5m/s², hence velocity increases by 5m/s for every unit of time (i.e. 1 second)

this is useful because if you know the gradient of any function you can figure out the function's rate of change(this is in both methods and spesh course!!) for specific values of either variable involved in the function. However in VCE physics its most likely that the rate of change for a function will remain a constant (i.e. original function is linear; y=mx+c, where m is a constant).