Presentation on theme: "Graphing Motion Position vs. Time Stationary objects"— Presentation transcript:
1 Graphing Motion Position vs. Time Stationary objects Position is same at every time (d = 0)So speed = 0Stationary objects
2 Graphing Motion Objects with constant speed PositiontPosition changes same amount every intervalIf it moves 2m in 1st second, it will move 2m every secondObjects with constant speed
3 Graphing Motion Objects with constant velocity PositiontThe slope is the change in position/ change in timeThat’s the speed or velocity!KEY FINDING: Slope of position/time graph is the speed or velocityNegative slope: object is moving in the negative directionObjects with constant velocityChange in positionChange in time
4 Interpreting Graphs What’s going on here? Starts in a positive positionMoves forward with constant speedStops for a whileGoes backward with constant speedGoes forward with constant speed to the origin (x = 0)What’s going on here?Positiont
5 Graphing Speed vs. TimeFor constant speed (could be sitting still, could be moving), speed doesn’t changeGraph is just a flat lineREMEMBER: This is just the slope of the position/time graph!PositionSpeedCase 2: Positive Constant SpeedCase 2: Positive Constant VelocityCase 1: No MotionCase 1: No Motiontt
6 Area under the curveQuestion: What does the area under the Velocity vs. Time graph tell you?4321Speed (m/s)Time (s)Answer: velocity x time = distance
7 Area under the curve It works for changing velocity, too! 4321Speed (m/s)Time (s)What is the total displacement?Area of the triangle: ½ * 4 * 4 = 8 meters
8 What’s happening here? We call it Acceleration Getting faster and fasterSlope increases, therefore…Speed increasesWe call it AccelerationSpeedtPositiont
9 Acceleration Notes Acceleration is any change in speed or direction. Acceleration occurs when an object speeds up, slows down (or changes direction– we’ll see this later)
10 Acceleration NotesUniform (or constant) acceleration: when an object accelerates at a constant rate over a period of time.Acceleration = change in velocity/time intervalSpeedt
11 Acceleration NotesMathematically: a = Δv = “change in velocity” v = final velocity vo = initial velocityUnits: (m/s) or m s s2Δv = v -vott
12 Acceleration NotesExample: A car starts out traveling at 10 m/s and accelerates to 19 m/s in a time of 3 seconds. What is the acceleration of the car?a = vf –vi = 19 m/s – 10 m/s = 3 m/s t 3sThe car accelerates at 3 m/s2.
13 Finding Acceleration on a Velocity Graph For linear change in velocity, acceleration is the slope of the velocity graphPositive slope, so positive accelerationSpeedSlope = accel = 0Negative slope, so neg. acceleration (sometimes called “deceleration”t
14 Average SpeedIf the speed is changing linearly (constant acceleration)Average speed is just the average of the initial and final speedsvave = v + votVVaveVo
15 Average Speed: Careful! If I accelerate uniformly from 10 to 20 mph (miles per hour), what’s my average speed?Constant acceleration: ½ * ( ) = 15 mphIf I drive 10 mph for 10 miles and 20 mph for 10 miles, what’s my average speed?13.3 mph!Not constant acceleration, so not 15 mph!!!