CPO ScienceFoundations of PhysicsChapter 9
Unit 1: Measurement and MotionChapter 4: Acceleration in a Straight Line• 4.1 Acceleration• 4.2 A Model for Accelerated Motion• 4.3 Free Fall and the Acceleration dueto Gravity
Chapter 4 Objectives1. Calculate acceleration from the change is speedand the change in time.2. Give an example of motion with constantacceleration.3. Determine acceleration from the slope of thespeed versus time graph.4. Calculate time, distance, acceleration or speedwhen given three of the four variables.5. Solve two-step accelerated motion problems.6. Calculate height, speed, or time of flight in freefall problems.7. Explain how air resistance makes objects ofdifferent masses fall with different accelerations.
Chapter 4 Vocabulary Terms• acceleration• m/sec 2• delta D• constant acceleration• uniform acceleration• slope• term• initial speed• free fall• acceleration due togravity (g)• time of flight• friction• air resistance• terminal speed
Key Question:4.1 AccelerationHow is the speed of the ball changing?*Students read Section 4.1 AFTER Investigation 4.1
4.1 Acceleration of a carAcceleration is the rate ofchange in the speed of anobject.
4.1 Acceleration vs. Speed• Positive accelerationand positive speed
4.1 Acceleration vs. Speed• Negative accelerationand positive speed
4.1 AccelerationAcceleration(m/sec 2 )a = DvDtChange in speed (m/sec)Change in time (sec)
4.1 Calculate Acceleration• A student conducts an• acceleration experiment bycoasting a bicycle down asteep hill.• The student records the speedof the bicycle every second forfive seconds.• Calculate the acceleration ofthe bicycle.
4.1 Acceleration and Speed• Constant acceleration is different from constantspeed.• Motion with zero acceleration appears as astraight horizontal line on a speed versus timegraph.zero accelerationconstant speed
4.1 Acceleration and Speed• Constant acceleration is sometimes calleduniform acceleration.• A ball rolling down a straight ramp has constantacceleration.constant accelerationincreasing speed
4.1 Acceleration and Speed• An object can have acceleration, but no speed.• Consider a ball rolling up a ramp.• As the ball slows down, eventually its speedbecomes zero.constant negativeaccelerationdecreasing speed
4.1 Slope and Acceleration• Use slope to recognize whenthere is acceleration in speedvs. time graphs.— Level sections (A) on the graphshow an acceleration of zero.— The highest acceleration (B) isthe steepest slope on thegraph.— Sections that slope down (C)show negative acceleration(slowing down).
4.2 A Model for Accelerated MotionKey Question:How do we describe and predict acceleratedmotion?*Students read Section 4.2 AFTER Investigation 4.2
4.2 Slope of a graph• The slope of a graph is equal tothe ratio of rise to run.• On the speed versus timegraph, the rise and run havespecial meanings, as they didfor the distance versus timegraph.• The rise is the amount thespeed changes.• The run is the amount the timechanges.
4.2 Acceleration and slope• Acceleration is the change in speed over the change intime.• The slope of the speed versus time graph is theacceleration.
4.2 Calculate acceleration• The following graphshows the speed of abicyclist going over ahill.• Calculate the maximumacceleration of thecyclist and say when inthe trip it occurred.
4.2 Solving Motion Problems
4.2 Solving Motion Problems
4.2 Calculate speed• A ball rolls at 2 m/sec ontoa ramp.• The angle of the rampcreates an acceleration of0.75 m/sec 2 .• Calculate the speed of theball 10 seconds after itreaches the ramp.
4.2 Solving Motion Problemsinitial position distance if at constant speeddistance to add or subtract,depending on acceleration
4.2 Calculate position• A ball traveling at 2 m/sec rolls onto a rampthat tilts upward.• The angle of the ramp creates anacceleration of -0.5 m/sec 2 .• How far up the ramp does the ball get at itshighest point?• (HINT: The ball keeps rolling upward until itsspeed is zero.)
4.2 Solving Motion Problems
4.2 Calculate time• A car at rest accelerates at 6 m/sec2.• How long does it take to travel 440 meters(about a quarter-mile) and how fast is the cargoing at the end?
4.2 Calculate position• A ball starts to roll down a ramp withzero initial speed.• After one second, the speed of theball is 2 m/sec.• How long does the ramp need to beso that the ball can roll for 3seconds before reaching the end?
4.3 Solving Problems with Free Fall
4.3 Calculate height• A stone is dropped downa well and it takes 1.6seconds to reach thebottom.• How deep is the well?• You may assume theinitial speed of the stoneis zero.
4.3 Air Resistance and Mass• The acceleration due to gravity does notdepend on the mass of the object which isfalling.• Air creates friction that resists the motion ofobjects moving through it.• All of the formulas and examples discussedin this section are exact only in a vacuum(no air).
4.3 Terminal Speed• You may safely assume that a = g =9.8 m/sec 2 for speeds up to severalmeters per second.• The resistance from air frictionincreases as a falling object’s speedincreases.• Eventually, the rate of acceleration isreduced to zero and the object fallswith constant speed.• The maximum speed at which anobject falls when limited by airfriction is called the terminal speed.
4.3 Free Fall and Acceleration due toKey Question:GravityHow do you measure the acceleration of a fallingobject?*Students read Section 4.3 BEFORE Investigation 4.3
Application: Antilock Brakes