### Motion GraphsEdit

All right ladies and gentlemen, let's start the commotion as I guide you through my wiki page all about Motion Graphs!

Drawing graphs is a very useful means of presenting information - and making it easily understood. Changes and patterns can be quickly recognized - it is not surprising that graphical systems are chosen when data needs to be presented and taken in and absorbed very quickly.....

In physics, we often use these graphs to present objects in motion. These graphs are called **motion graphs**. The three most common types of **motion graphs** are **acceleration vs. time graphs**, **velocity vs. time graphs** and **displacement vs. time graphs**.

### Velocity vs. Time GraphsEdit

First, we will talk about velocity vs. time graphs. Here is an example of one which shows constant acceleration:

To find the **acceleration** from a velocity vs. time graph just divide the change in velocity (y-axis) by the change in time (x-axis). Use this to help you remember:

The principle is that the slope of the line on a velocity-time graph reveals useful information about the acceleration of the object. Whatever characteristics the acceleration has, the slope will exhibit the same (and vice versa).

If the acceleration is zero, then the slope is zero (i.e., a horizontal line). If the acceleration is positive, then the slope is positive (i.e., an upward sloping line). If the acceleration is negative, then the slope is negative (i.e., a downward sloping line).

#### Finding the Distance of an Object Using Velocity vs. Time GraphsEdit

A great tool we can use from studying velocity vs. time graphs is to find the distance when we have time plotted on our x-axis and velocity plotted on the y-axis. To do this we have to keep in mind the following equations:

**distance= (velocity)(time)**

**velocity=(distance)/(time)**

**time=(velocity)/(distance)**

When looking at a velocity vs. time graph, we can apply the first equation to find the distance. We do this by simply finding the area under the line of the graph. This graph is an example of the area under the line:

**Note:** The area will not always be a rectangle. This only occurs if the object's velocity is not changing. If the object is acceelerating at a constant rate, you can form a right triangle and find the area of it.

### Acceleration vs. Time GraphsEdit

When we are comparing how acceleration changes as time changes we are looking at an acceleration vs time graph.

#### Motion Graphs Showing Constant AccelerationEdit

As shown here, all graphs with constant acceleration will have a slope of 0:

Here is a description of the graphs below:

a) shows the graph for an object which is either stationary or traveling at a constant velocity. Either way, the acceleration is zero over time.

b) shows the graph for an object moving at a constant acceleration. In this case the acceleration is positive - remember that it can also be negative.

We can obtain the velocity of a particle at some given time from an acceleration time graph - it is just given by the area between the graph and the time-axis. In the graph below, showing an object at a constant positive acceleration, the increase in velocity of the object after 2 seconds corresponds to the shaded portion.

### Displacement vs. Time GraphsEdit

Displacement is defined as how far an object is from wherever it started. Think of it like this:

A bike rider starts biking from home. He heads north 3 kilometers and gets hit head on by a truck which knocks him back 1 kilometer south. He breaks every bone in his body and is never found... Whats his displacement?

... THATS RIGHT! His displacement is 2 kilometers

Displacement can be presented as a motion graph. Here are some examples to make you feel right at home with **displacement vs. time** motion graphs!

a) shows the graph for an object stationary over a period of time. The slope is zero, so the object has zero velocity. The object is not getting any farther away from its starting point.

b) shows the graph for an object moving at a constant velocity. You can see that the displacement is increasing as time goes on. The slope, however, stays constant (remember: its the slope of a straight line), so the velocity is constant. Here the slope is positive, so the object is moving in the direction we have defined as positive.

c) shows the graph for an object moving at a constant acceleration. You can see that both the displacement and the velocity (slope of the graph) increase with time. The slope is increasing with time, thus the velocity is increasing with time and the object is accelerating.

## Sample QuestionsEdit

*Note: This sample question should help sum up all of the knowledge given about reading motion graphs on this wiki page!*

II.

1. For each of the four graphs below indicate on the graph:

a) the sign of the velocity

b) whether the velocity is increasing or decreasing

c) the sign of the acceleration

II. Mr. G.K. walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North as shown in the diagram below.

What is Mr. G.K.'s total displacement?

IV. Describe the motion depicted by the following velocity-time graphs. Use + and - to describe where the velocity is increasing and decreasing. (Mark at points A,B,C)

Solutions to David's killer practice problems!

## ReferencesEdit

1) http://en.wikibooks.org/wiki/FHSST_Physics_Rectilinear_Motion:Graphs

2) http://en.wikibooks.org/wiki/FHSST_Physics_Rectilinear_Motion:Graphs

3) http://www.stvincent.ac.uk/Resources/Physics/Speed/speed/motgraphs.html

4) http://www.stvincent.ac.uk/Resources/Physics/Speed/speed/motgraphs.html

5) http://www.physicsclassroom.com/Class/1DKin/U1L4a.html http://www.physicsclassroom.com/Class/1DKin/U1L4a.html

6) http://acept.la.asu.edu/courses/phs110/course_info/sample_tests/test1/sample_test.html

7) http://www.sparknotes.com/testprep/books/sat2/physics/

8) http://www.regentsprep.org/Regents/core/questions/topics.cfm?Course=PHYS