Presentation on theme: "Peet - period 3 Do Now The position-time graph above represents the motion of a basketball coach during the last sixteen seconds of overtime. Determine."— Presentation transcript:
1Peet - period 3Do NowThe position-time graph above represents the motion of a basketball coach during the last sixteen seconds of overtime.Determine the total distance walked by the coach during these 16 seconds.Determine the resulting displacement of the coach during these 16 seconds.What was the fastest speed which the coach walked? During which time interval was he walking at this speed?
2Aim: How are velocity vs. time graphs analyzed? Peet - period 3Aim: How are velocity vs. time graphs analyzed?SWBAT:construct and interpret graphs of position, velocity, or acceleration versus time (S4.5.1.i)determine and interpret slopes and areas of motion graphs (S4.5.1.ii)
3Graphs of Motion Position (displacement) vs. Time Peet - period 3Graphs of Motion* the steeper the slope,the higher the speed (value of velocity)Position (displacement) vs. TimeSlope of position-time graph = velocity over that interval of timepositionpositionpositionpositiontimetimetimetimeSlope is zero∴velocity is zero(object at rest)Slope is positive∴velocity is constant, positiveSlope is negative∴velocity is constant, negativeSlope is curve∴velocity is not constant(object accelerating)
4Graphs of Motion Velocity vs. Time Peet - period 3Graphs of Motion* the steeper the slope,the higher the value of accelerationVelocity vs. TimeSlope of v-t graph = acceleration over that interval of timevelocityvelocityvelocityvelocitytimetimetimetimeSlope is zero∴acceleration is zero(at rest or with constant velocity)Slope is positive∴acceleration is constant, positiveSlope is negative∴acceleration is constant, negativeSlope is curve∴acceleration is not constant
5Peet - period 3BEWARE: Just because the slope of the v-t graph is negative (acceleration negative), does not always mean the object in motion is decelerating (slowing down)!Nor does the slope being positive mean the object is accelerating (speeding up)Slowing downSpeeding upvelocitytimeSlowing downSpeeding up
6Graphs of Motion Velocity vs. Time Peet - period 3Graphs of Motion* Sum of areas with signs: displacement* Sum of areas without signs: distanceVelocity vs. TimeArea under v-t graph = displacement and/or distance over that interval of timevelocityvelocityvelocitytimetimetimeLine along x-axisNo area∴ no displacementLine above x-axisPositive areaLine below x-axisNegative area
8What is the acceleration from: t = 0s to t = 4s? t = 4s to t = 8s? Peet - period 3What is the acceleration from:t = 0s to t = 4s?t = 4s to t = 8s?t = 8s to t = 10s?What is the distance traveled? Is it the same as the object’s displacement?
13Two Equations from Monday Peet - period 3Two Equations from MondayPosition with constant acceleration:Velocity with constant acceleration:
14Equations of Motion for Uniform (Constant) Acceleration Peet - period 3Equations of Motion for Uniform (Constant) AccelerationEquationVariablesInitial Conditionst, vf, avit, df, adi, vidf, vf, a
15Peet - period 3Example: 3.27A race car travels on a racetrack at 44 m/s and slows at a constant rate to a velocity of 22 m/s over 11 s. How far does it move during this time?
16Peet - period 3Problem 3.28A car accelerates at a constant rate from 15 m/s to 25 m/s while it travels a distance of 125 m/ How long does it take to achieve this speed?
17Peet - period 3Problem 3.29A bike rider pedals with constant acceleration to reach a velocity of 7.5 m/s over a time of 4.5 s. During the period of acceleration, the bike’s displacement is 19 m. What was the initial velocity of the bike?
18Peet - period 3Problem 3.30A man runs at a velocity of 4.5 m/s for 15 minutes. When going up an increasingly steep hill, he slows down at a constant rate of 0.05 m/s2 for 90.0 seconds and comes to a stop. How far did he run?