Cornell Notes 2-5 Graphing Motion February 19, 2016 Page 135 & 137

Linear and Non-Linear Graphs Linear graphs go in a straight line. They represent relationships with the formula y=kx k is the slope of the line. You can figure out slope by dividing change in y over change in x (10-5)/(2-1)=5/1=5

Non-Linear Graphs Non-linear graphs go in curves They usually have formulas like y=kx2

The Rectangle Method You can use the rectangle method to make predictions. Just find the key term on the axis, draw a straight line up to the graph, and another straight line to the other axis. If you need to, you can extend the graph in either direction to help make your prediction

Position vs Time Graphs In a position vs time graph, time is on the x and position on the y.

Speed vs Time Graphs In a Speed vs time graph, time is on the x and speed on the y.

When Something is Not Moving PvT is a Horizontal Line SvT is a Horizontal Line at 0 Car isn’t moving, so its speed is 0 m/s Car stays at 5 m

When Something is Moving at a Constant Speed PvT is a Straight Line SvT is a Horizontal Line Car moves 2 m every second! Car’s speed is 2 m/s

When Something is Moving Backwards at a Constant Speed PvT is a Straight Line Going Down SvT is a Horizontal Line Car moves 2 m every second, but backwards! Car’s speed is 2 m/s

Speed vs Speed Faster Objects Have Steeper Slopes Faster Objects Are Higher Up 2 m/s 2 m/s 1 m/s 1 m/s

Changing Speeds (Speeding Up) PvT Curves! At Constant Acceleration, SvT is a Straight Line Slope Gets Steeper! Speed is increasing by 1 m/s every second

Changing Speeds, Slowing Down PvT Curves SvT is Now Going Backwards Car moving 1 m/s slower every second Still moving forward, but slower every second

Slopes on PvT Graphs The slope on a PvT graph shows the speed of the object. To calculate slope, do the following Pick two points on the graph Subtract the y-values of the points, the point on the right going first (y2-y1) Subtract the x-values of the points, the point on the right going first (x2-x1) Divide the y’s by the x’s (Rise over run)

Example (120 - 60)  (80 - 40) = 60  40 = 1.5 cm/s Y Goes Up 20 X Goes Up 40 (120 - 60)  (80 - 40) = 60  40 = 1.5 cm/s

Quick Summary for PvT’s If the line is horizontal, then the object graphed is not moving If the line is linear, then the object graphed I moving at a constant speed If the line is non-linear, then the object’s speed is changing The slope of a PvT graph is the object’s speed For constant speed, objects with greater speeds have steeper slopes

Quick Summary for SvT’s If the line is at zero, then the object graphed is not moving If the line is horizontal, then the object graphed is moving at a constant speed If the line is straight, then the object’s speed is changing at a constant rate

Story Time!