Chapter 3 - Motion Along A Straight Line

Chapter 3 - Motion Along a Straight LineChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand Speed“I can calculate themotion of heavenlybodies, but not themadness of people.”- Isaac NewtonDavid J. StarlingPenn State HazletonPHYS 211Acceleration

Position, Displacement and DistanceKinematics is the study of motion.Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationPosition is the coordinate x(t) of the object in question.

Position, Displacement and DistanceChapter 3 - MotionAlong a Straight LineDisplacement x is the change in the position ofPosition, Displacementand Distancean object. x x2 x1 (can be negative!)Average Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Position, Displacement and DistanceChapter 3 - MotionAlong a Straight LineDisplacement x is the change in the position ofPosition, Displacementand Distancean object. x x2 x1 (can be negative!)Average Velocity andSpeedInstantaneous Velocityand SpeedAccelerationWhat is the displacement from time t1 0 to t2 4?

Position, Displacement and DistanceDistance d is the total amount of ground an objectcovers during its motion.Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Position, Displacement and DistanceDistance d is the total amount of ground an objectcovers during its motion.Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationIs distance ever less than displacement?

Position, Displacement and DistanceChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedSummary:IPosition is a function: x(t)IDisplacement is the change in position: x x2 x1IDistance is how much ground is covered: d, alwayspositive!Acceleration

Position, Displacement and DistanceChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceLecture Question 3.1A race car, traveling at constant speed, makes one laparound a circular track of radius r in a time t. Which one ofAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationthe following statements concerning this car is true?(a) The displacement is constant.(b) The instantaneous velocity is constant.(c) The average speed is the same over any time interval.(d) The average velocity is the same over any time interval.(e) The average speed and the average velocity are equalover the same time interval.

Average Velocity and SpeedAverage Velocity vavg is the displacement dividedby the time interval.vavg Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeed xx2 x1 tt2 t1Instantaneous Velocityand SpeedAcceleration

Average Velocity and SpeedFind the average velocity:Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Average Velocity and SpeedFind the average velocity:Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationvavg x2 x12 ( 4) 2 m/st2 t14 1

Average Velocity and SpeedChapter 3 - MotionAlong a Straight LineAverage Speed savg is the distance divided by thePosition, Displacementand Distancetime interval.Average Velocity andSpeedsavg d 0 tInstantaneous Velocityand SpeedAcceleration

Average Velocity and SpeedChapter 3 - MotionAlong a Straight LineAverage Speed savg is the distance divided by thePosition, Displacementand Distancetime interval.Average Velocity andSpeedsavg d 0 tInstantaneous Velocityand SpeedAccelerationHow does savg compare to vavg ?

Average Velocity and SpeedChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedYou drive for 8.4 km down a road at 70 km/h before you runInstantaneous Velocityand Speedout of gas. You walk another 2.0 km in 30 minutes. What isAccelerationyour overall displacement during this time?(a) 2.0 km(b) 2.1 km(c) 10 km(d) 590 km

Average Velocity and SpeedChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceYou drive for 8.4 km down a road at 70 km/h before you runout of gas. You walk another 2.0 km in 30 minutes. HowAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationlong does this take?(a) 0.12 hr(b) 0.50 hr(c) 30.12 min(d) 0.62 hr(e) 30.12 hr

Average Velocity and SpeedChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceLecture Question 3.2You drive for 8.4 km down a road at 70 km/h before you runout of gas. You walk another 2.0 km in 30 minutes. What isyour average velocity during this time?(a) 4 km/hr(b) 17 km/hr(c) 37 km/hr(d) 70 km/hrAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Instantaneous Velocity and SpeedInstantaneous velocity v is the average velocityduring an infinitely short time period. xdx v lim t 0 tdtChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Instantaneous Velocity and SpeedInstantaneous velocity v is the average velocityduring an infinitely short time period. xdx v lim t 0 tdtChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Instantaneous Velocity and SpeedChapter 3 - MotionAlong a Straight LineLike average velocity, instantaneous velocity v hasPosition, Displacementand Distancea “direction” and can be negative.Average Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Instantaneous Velocity and SpeedChapter 3 - MotionAlong a Straight LineLike average velocity, instantaneous velocity v hasPosition, Displacementand Distancea “direction” and can be negative.Average Velocity andSpeedInstantaneous Velocityand SpeedAccelerationInstantaneous velocity is the slope of this curve at eachmoment in time!

Instantaneous Velocity and SpeedInstantaneous speed s is the average speedduring an infinitely short time period.d t 0 ts limChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Instantaneous Velocity and SpeedInstantaneous speed s is the average speedduring an infinitely short time period.d t 0 ts limThe magnitude of s is equal to the magnitude of v sinced x during a short period of time.s v dxdtChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Chapter 3 - MotionAlong a Straight LineAccelerationAverage acceleration aavg is the change invelocity divided by the time interval.Position, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand Speedaavg vv2 v1 tt2 t1Colonel J. P. Stapp in a rocket sled.Acceleration

AccelerationInstantaneous acceleration a is the averageacceleration during an infinitely short time period.Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration v t 0 ta lim

AccelerationInstantaneous acceleration a is the averageacceleration during an infinitely short time period.Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationd2 xdv v 2 t 0 tdtdta lim

AccelerationInstantaneous acceleration a is the averageacceleration during an infinitely short time period.Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAccelerationd2 xdv v 2 t 0 tdtdta lim

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.a aavgv2 v1 v2 v1 a tt2 t1Average Velocity andSpeedInstantaneous Velocityand Speed(1)Acceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.a aavgAlso,vavg v2 v1 v2 v1 a tt2 t1x2 x1 x2 x1 vavg tt2 t1Average Velocity andSpeedInstantaneous Velocityand Speed(1)Acceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.a aavgAlso,vavg v2 v1 v2 v1 a tt2 t1x2 x1 x2 x1 vavg tt2 t1To replace vavg , consider:Average Velocity andSpeedInstantaneous Velocityand Speed(1)Acceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.a aavgAlso,vavg v2 v1 v2 v1 a tt2 t1x2 x1 x2 x1 vavg tt2 t1To replace vavg , consider:11vavg v1 v v1 a t22Average Velocity andSpeedInstantaneous Velocityand Speed(1)Acceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.Average Velocity andSpeedInstantaneous Velocityand Speed1x2 x1 v1 t a t22(2)Acceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.Average Velocity andSpeedInstantaneous Velocityand Speed1x2 x1 v1 t a t22(2)Finally, if we eliminate t by combining Eqs. (1) and (2),we get:v2 v1 t aAcceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.Average Velocity andSpeedInstantaneous Velocityand Speed1x2 x1 v1 t a t22(2)Finally, if we eliminate t by combining Eqs. (1) and (2),we get:v2 v1 t a v2 v11v2 v1 2x2 x1 v1 aa2aAcceleration

Chapter 3 - MotionAlong a Straight LineAccelerationIn many cases, a constant. In this case, wePosition, Displacementand Distanceobtain three very useful equations.Average Velocity andSpeedInstantaneous Velocityand Speed1x2 x1 v1 t a t22(2)Finally, if we eliminate t by combining Eqs. (1) and (2),we get:v2 v1 t a v2 v11v2 v1 2x2 x1 v1 aa2av22 v21 2a(x2 x1 )(3)Acceleration

Chapter 3 - MotionAlong a Straight LineAccelerationPosition, Displacementand DistanceThe three constant acceleration equations are:Average Velocity andSpeedInstantaneous Velocityand SpeedAccelerationv2 v1 at21x2 x1 v1 t2 at22222v2 v1 2a(x2 x1 )where t1 0 so that t t2 t1 t2 .

Chapter 3 - MotionAlong a Straight LineAccelerationPosition, Displacementand DistanceThe three constant acceleration equations are:Average Velocity andSpeedInstantaneous Velocityand SpeedAccelerationv(t) v0 at1x(t) x0 v0 t at2222v v0 2a(x x0 )where t1 0, t2 t, x1 x0 and x2 x.

AccelerationObjects near the surface of Earth acceleratetoward the Earth with an acceleration of g 9.8m/s2 (ignoring air resistance).Chapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceAverage Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

AccelerationChapter 3 - MotionAlong a Straight LinePosition, Displacementand DistanceLecture Question 3.4An explorer accidentally drops a wrench over the side of herhot air balloon as it rises from the ground. The balloon’supward acceleration is 4 m/s2 with a a velocity of 2 m/s.Just after the wrench is released,(a) its acceleration is -5.4 m/s2 , its velocity is 2 m/s.(b) its acceleration is -5.4 m/s2 , its velocity is 0 m/s.(c) its acceleration is -9.8 m/s2 , its velocity is 2 m/s.(d) its acceleration is 5.4 m/s2 , its velocity is 0 m/s.(e) its acceleration is 5.4 m/s2 , its velocity is -2 m/s.Average Velocity andSpeedInstantaneous Velocityand SpeedAcceleration

Average Velocity v avg is the displacement divided by the time interval. v avg x t x 2 x 1 t 2 t 1. Chapter 3 - Motion Along a Straight Line Position, Displacement and Distance Average Velocity and Speed Instantaneous Velocity and Speed Acceleration Average Velocity and Speed Find the average velocity: v avg x 2 x 1 t 2 t 1 2 ( 4) 4 1