# What does velocity mean in motions graphs?

Feb 17, 2015

Velocity is the change in position occurring over a change in time. Change in position is known as displacement, and is represented by $\Delta d$, and change in time is represented by $\Delta t$, and velocity is represented by $\frac{\Delta d}{\Delta t}$.

In position vs. time graphs, time is the independent variable and is on the x-axis, and position is the dependent variable and is on the y-axis. The velocity is the slope of the line, and is the change in position/change in time, as determined by $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ = $\frac{{d}_{2} - {d}_{1}}{{t}_{2} - {t}_{1}}$ =$\frac{\Delta d}{\Delta t}$.

The following position vs. time graph shows the different possibilities when the velocity is constant. Constant velocity is represented by a straight line on a position vs. time graph.

On the graph, Line A represents constant negative velocity. Lines B and D represent constant positive velocity. The steeper slope of Line B indicates a faster velocity than D. Line C indicates a constant velocity of zero, meaning the object is at rest. The position vs. time graph below indicates that the motion of an object is not constant. Suppose it is a car. For the first 10s, it travels at a constant positive velocity. For the next 5s, its velocity is zero, meaning it has stopped. For the next 25s it travels at a constant negative velocity, and for the last 15s, it travels at a constant positive velocity and returns to its initial position. 