# Graphing basics EQ: How can motion be measured, described, and analyzed with the use of a graph?

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Graphing basics EQ: How can motion be measured, described, and analyzed with the use of a graph?

Graphin g Specific features of the motion of objects are demonstrated by the shape and the slope of the lines on a graph. We will analyze 2 types of graphs 1. Position vs time graph 2. Velocity vs time graph

the shape of the line on the graph (straight, curving, steeply sloped, mildly sloped, etc.) is descriptive of the object's motion. the slope of the line on a is: Calculating slope Pick two points on the line and determine their coordinates. Determine the difference in y-coordinates of these two points (rise). Determine the difference in x-coordinates for these two points (run). Divide the difference in y-coordinates by the difference in x- coordinates (rise/run or slope). Graphin g

Graphing Motion Position vs time Consider a car moving at a constant velocity of +5 m/s for 5 seconds, abruptly stopping, and then remaining at rest (v = 0 m/s) for 5 seconds. The line on the position vs. time graph has a slope of +5 meters/1 second for the first five seconds. The slope of the line on the graph equals the velocity of the car. During the last 5 seconds (5 to 10 seconds), the line slopes up 0 meters. The slope of the line is 0 m/s - the same as the velocity during this time interval.

Position changing at a constant rate = Constant velocity Slow rightward Fast rightward Slow leftwardFast leftward Position changing at a varying rate = Changing velocity Slow to fast Leftward Fast to Slow leftward Slow to Fast rightward Slope = Velocity Slope = direction of velocity

Graphing Motion Velocity vs time Constant Velocity Consider a car moving with a constant, rightward (+) velocity of +10 m/s. A car moving with a constant velocity is a car with zero acceleration. Changing Velocity A car with a changing velocity will have an acceleration acceleration = zero, then the is a horizontal line acceleration is positive, then the slope is positive (i.e., an upward sloping line). acceleration is negative, then the slope is negative (i.e., a downward sloping line).

Velocity changing = Constant acceleration No – Zero acceleration Slope on a V-T graph = acceleration

The object’s velocity is increasing in the positive direction The object has a positive acceleration Same motion described by 2 different graphs P-T graph V-T graph

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