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Notes on. Position-time graphs. Position-time graphs. Position value is recorded as the vertical (y) component Time value is recorded as the horizontal The point (4,-8) means you are at -8 units from the central reference point at the 4 second mark. Position-time graph.

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## Position-time graphs

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**Notes on**Position-time graphs**Position-time graphs**• Position value is recorded as the vertical (y) component • Time value is recorded as the horizontal • The point (4,-8) means you are at -8 units from the central reference point at the 4 second mark**Position-time graph**Where is the object at the 3 second mark? 9 second mark?**What information does the graph tell you about motion**• Shape of the line • Straight-vs-curved • Tilt of the line • Flat-vs-slanted • Tilted upward-vs-tilted downward • Vertical lines • Placement of the line • Start position • Postive-vs negative territory**Position Time graphs**• Graph indicates • Positive motion • Constant velocity • Between fast and slow rate of motion**At rest**• How does a graph indicate that the object does not move**Which line shows no motion?Which line shows fastest rate of**motion?**Graph indicates**Non-constant velocity Positive motion Getting faster**Graph indicates**Negative motion Non-constant velocity Getting faster**Graph indicates**Negative motion Non-constant velocity Slowing down**Forward, backward, or stopped**• If the graph is horizontal, then no motion has occurred. • The position (vertical) value did not change over time • If the final position is more positive than the initial position , it moved forward • If the final position is less positive than initial position, it moved backward**Is the object moving at a constant rate?**• Constant velocity means the rate of motion does not change over time • Graphs show constant velocity by creating a straight line. • Angle (tilt) of line does not matter**How fast is it going?**• Constant velocity can occur in any direction • Being stopped gives you a constant velocity of zero (0). • The tilt of a straight line will indicate forward, or backward motion • Slope of the line is a measure of the object’s velocity • The amount of tilt will indicate how fast th object goes**What if it is not a straight line?**• Then the velocity is not constant • If the velocity changes over time the car accelerates • Any change in velocity indicates acceleration • On a P-T graph, acceleration is indicated by a curved line**It is getting faster or slower?**• Tangent lines • Pick 2 point along section of graph • Draw tangent lines • If the slope of line increases, then object is getting faster • Divide section up into equal 2 blocks of time. • Compare the displacement in each • If amount of displacement increases, it is getting faster**Tangent line**• Line that touches a graph at only one point**Mathematical method to determine slope of tangent lines**• Determine the rate of change • Derivatives in calculus**Draw the graph**• Draw a graph that would represent the following motion: • Positive Motion • Non-Constant Velocity • Slowing Down**Information from graphs**• For each section with the same type of motion, you should be able to determine: • Is the object moving forward, backward, or stopped • Is the motion constant or not? • If constant, is the rate of motion fast or slow? • If not constant, is the object getting faster or slower?**Position-Time**4 2 5 3 6 1 2**Position time graph**• Each point on the graph indicates the position of the object at a certain time • Shows both distance and displacement • Y-axis indicates position • X-axis indicates time**Most graphs are made from a combination of different types**of motions**What you should be able to tell me about the graph**Whether object is moving or not Which direction it moves Whether motion is constant or not Whether object speeds up or slows**Creating a graph from written information**• Draw a copy on a piece of paper**In the next graph…**• You will create a graph that represents the following motion • Section 1- starts at the -2 meter position and moves with slow positive constant velocity • Section 2- moves with fast negative constant velocity**Information for next graph…**• Section 3- moves with positive non-constant velocity and is getting faster • Section 4- moves with a constant velocity of zero • Section 5 – moves with a negative non-constant velocity and is slowing down**Example #1**• Starting from a position of (-3). • Object speeds up, moving forward to the origin • Object maintains constant velocity moving forward, reaches (4) • Object slows down, moving forward, reaches (6) • Object Stops for several seconds • Object speeds up moving backwards**Assumption**• If the question does not specify times, assume that the displacement of interest is over the entire graph**What is the velocity of the car during the first 1.5 second?**• Is it constant • Is it relatively fast or slow? • How do you find its actual value?**To answer the initial problem**• (3 – 0)(m) / (1.5 – 0)(s) = 3 m/s Find the rest of the constant velocity values shown on the graph**Calculation of a constant velocity**• Slope of the line = steepness • To determine slope, find the rise over run • Rise = change in the y valuesbetween initial and final points Run change in the x values • V = (y2 –y1) / (x2 – x1)**Slope of the line**• Constant velocity is demonstrated by a slanted straight line on a P-T graph • The steepness indicates how fast the object moves • To measure the steepness of a line, calculate the slope**How to calculate the slope**Rise= change in the position Run= change in the time Slope = Rise / Run**Calculating the velocity**• Use (y2-y1) / (x2 – x1) to calculate the slope (velocity) • Organization of information • Starts with identification of x and y values

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