Jill Luckey Beaufort Academy

What do you already know? In Math classes, you have learned how to make graphs. You have also learned that the SLOPE of the line on a graph can be found by taking  Y /  X. The Y axis is also called the “Rise” The X axis is also called the “Run” Therefore, SLOPE is also Rise/Run

Relationship of Units to Graphs What units do you know that consist of a numerator unit and a denominator unit? One example is for Density Density is mass / volume If you graphed mass on the Y axis and volume on the X axis, the slope would show you Density

PICTURE THIS: Let’s say you cut up a wooden dowel into 5 pieces, each piece having a different length Let’s say you measured the mass of each piece and the volume of each piece and plotted them against each other Let’s take that data…

Data Table for Wood Density Piece number Mass Volume g 16 cm g 20 cm g 24 cm g 28 cm g 32 cm3

Let’s Graph That…

Are there other units like that? How about speed (let’s call it velocity starting now) Velocity has to have magnitude and direction (v = d/t) since it is a vector quantity and all vectors have to have magnitude and direction How about Acceleration (a = v/t)

The Three Categories of Motion Graphs We graph motion to help us better understand what the moving object is doing One is Displacement One is Velocity One is Acceleration So, we can have Displacement-Time graphs, Velocity-Time graphs, and Acceleration-Time graphs

Displacement-Time Graphs There are 3 types of displacement –time graphs. Each tells us something different about the motion of an object, and the “curve” of the line on the graph communicates that info easily

What does this d-t graph tell you? That as each second passes,… The object has no additional displacement So the object must not be moving!

What does this d-t graph tell you? That as time passes,… More and more displacement occurs, but at a very regular rate So the object must be moving at constant velocity

What does this d-t graph tell you? That as time passes… The amount of displacement covered each second increases compared with the prior time Which is typical of an accelerating object

Now, Let’s move on to Velocity- Time Graphs. What does this graph tell you?

What does this v-t graph tell you?

And what might this v-t graph tell you?

Summary of Motion Graphs – Slope = Rise / Run If d is in m and t is in s,… If v is in m/s and t is in s,... If a is in m/s 2 and t is in s,… then the slope is m / s which is velocity then the slope is m / s 2 which is acceleration then the slope is m / s 3 and is meaningless v a x

Summary of Motion Graphs – Area = Base x Height (or ½ b*h) If d is in m and t is in s,… If v is in m/s and t is in s,... If a is in m/s 2 and t is in s,… Then the area under is m*s which is meaningless Then the area under is m/s * s which is m which indicates displacement Then the area under is m/s 2 * s which is m/s which indicates velocity x d v

Review On a d-t graph, a horizontal line shows a diagonal line shows a curving line shows On a v-t graph, a horizontal line shows a diagonal line shows a curving line shows That there is no change in position over time; the object is not moving That as time passes, equal distances are covered in equal time, so there is constant v That as time passes, greater and greater distances are covered for every second of travel (acceleration) That there is no change in velocity over time; the object is moving at a constant rate That as time passes, velocity increases at a regular rate (acceleration) That as time passes, the velocity increases at a greater and greater rate (incr. accel)