<meta http-equiv="refresh" content="1; url=/nojavascript/">

# Graphing Motion

## Use the slope of a graph to determine instantaneous velocity or acceleration for an object.

0%
Progress
Practice Graphing Motion
Progress
0%
Graphing Motion

Students will learn how to graph motion vs time. Specifically students will learn how to take the slope of a graph and relate that to the instantaneous velocity or acceleration for position or velocity graphs, respectively. Finally students will learn how to take the area of a velocity vs time graph in order to calculate the displacement.

### Key Equations

For a graph of position vs. time. The slope is the rise over the run, where the rise is the displacement and the run is the time. thus,

Slope = $v_{avg} = \frac{\Delta x}{\Delta t}$

Note : Slope of the tangent line for a particular point in time = the instantaneous velocity

For a graph of velocity vs. time. The slope is the rise over the run, where the rise is the change in velocity and the run is the time. thus,

Slope = $a_{avg} = \frac{\Delta v}{\Delta t}$

Note : Slope of the tangent line for a particular point in time = the instantaneous acceleration

Guidance
• One must first read a graph correctly. For example on a position vs. time graph (thus the position is graphed on the y-axis and the time on the x-axis) for a given a data point, go straight down from it to get the time and straight across to get the position.
• If there is constant acceleration the graph $x$ vs. $t$ produces a parabola. The slope of the $x$ vs. $t$ graph equals the instantaneous velocity. The slope of a $v$ vs. $t$ graph equals the acceleration.
• The slope of the graph $v$ vs. $t$ can be used to find acceleration; the area of the graph $v$ vs. $t$ can be used to find displacement. Welcome to calculus!