Question

How to calculate the slope of position time graph?

Answer 1

Answer:

The slope of a position-time graph can be calculated as:

$m=\frac{\Delta y}{\Delta x}$

where

$\Delta y$ is the increment in the y-variable

$\Delta x$ is the increment in the x-variable

We can verify that the slope of this graph is actually equal to the velocity. In fact:

$\Delta y$ corresponds to the change in position, so it is the displacement, $\Delta s$

$\Delta x$ corresponds to the change in time $\Delta t$, so the time interval

Therefore the slope of the graph is equal to

$m=\frac{\Delta s}{\Delta t}$

which corresponds to the definition of velocity.