11 SECTION 2 Acceleration
NameCHAPTER 11ClassDateMotionSECTION2 AccelerationKEY IDEASAs you read this section, keep these questions in mind: What two things may change when an objectaccelerates? How can you calculate constant acceleration? How can graphs show acceleration?How Is Acceleration Related to Velocity?Acceleration occurs when an object changes velocity.Remember that velocity has both a speed and a direction.Therefore, acceleration also has two components: a magnitude and a direction. When the speed or the direction ofan object changes, the object is accelerating.READING TOOLBOXDefine As you read thissection, underline any wordsyou don’t know. When youlearn what they mean, writethe words and their definitionsin your notebook.ACCELERATION AND SPEEDAn object that changes speed is accelerating. Anaccelerating object may speed up or slow down. An objectthat is speeding up has a positive acceleration. An objectthat is slowing down has a negative acceleration.Suppose a cyclist starts peddling south and speeds updown the road. Every second, the velocity of the cyclistincreases by 1 m/s. After 1 s, the cyclist’s velocity is1 m/s south. After 2 s, the cyclist’s velocity is 2 m/s south.After 5 s, the cyclist’s velocity is 5 m/s south.You can describe the cyclist’s acceleration by sayingthat his velocity is increasing by one meter per secondper second (1 m/s/s or 1 m/s2). In this case, the cyclist isspeeding up. Therefore, his acceleration is 1 m/s2 south.1:00002:00003:00004:00005:00001 m/s2 m/s3 m/s4 m/s5 m/sREADING CHECK1. Describe A car slowsdown as it comes up to astop sign. Is its accelerationpositive or negative?EHHDBG@ EHL K 2. Identify RelationshipsWhat happens to the cyclist’sspeed as time increases?This cyclist’s speed increases by 1 m/s every second. Therefore, his acceleration is1 m/s/s, or 1 m/s2.Copyright by Holt, Rinehart and Winston. All rights reserved.Interactive Reader237Motion
NameSECTION 2ClassDateAcceleration continuedKXcb 8Yflk @kBrainstorm Make a list of10 examples of acceleration.With a partner or in a smallgroup, identify how velocityis changing in each example.ACCELERATION AND DIRECTIONAn object that changes direction is accelerating, evenif its speed is constant. For example, the skaters in thefigure below are moving at a nearly constant speed.However, they must change direction to stay on thetrack. As they go around the curves in the track, theyaccelerate.EHHDBG@ EHL K 3. Identify Give twoways the skaters may beaccelerating.As these skaters change direction, they accelerate, even if their speeddoesn’t change.CENTRIPETAL ACCELERATIONREADING CHECK4. Explain How can anobject moving in a circularpath be accelerating if itsspeed does not change?Imagine moving at a constant speed in a circle. At eachpoint in the circle, your direction is changing. Therefore,you are constantly accelerating, even though your speeddoes not change. You are experiencing centripetal acceleration. Centripetal acceleration is the acceleration thatoccurs when an object moves in a circular path.You may think that centripetal acceleration is not verycommon. In fact, you and everything around you areexperiencing centripetal acceleration right now. This isbecause Earth is rotating on its axis. As Earth rotates, itssurface—and everything on it—travels in a circular path.Therefore, it experiences centripetal acceleration.Earth itself also experiences centripetal accelerationas it orbits the sun. Our moon is constantly acceleratingas it orbits Earth. In fact, every object that orbits anotherobject is experiencing centripetal acceleration.Copyright by Holt, Rinehart and Winston. All rights reserved.Interactive Reader238Motion
NameSECTION 2ClassDateAcceleration continuedHow Can You Calculate Acceleration?For an object moving in a straight line, accelerationoccurs only because of changes in speed. Therefore, youcan calculate the object’s acceleration if you know itsspeed at two different times. You can use the equationbelow to calculate acceleration:final speed initial speedacceleration time va tIn this equation, the symbol “delta” ( ) means “changein.” You calculate acceleration by dividing the change inspeed by the time in which the change occurred.If the acceleration is small, the velocity is changingslowly. For example, a person can accelerate at about2 m/s2. If the acceleration is large, the velocity is changingmore quickly. A sports car can accelerate at about7.2 m/s2.8g i XVa I] c c\5. Infer Can you use theequation to the left to calculate centripetal acceleration?Explain your answer.CALCULATING ACCELERATION FROM VELOCITYLet’s look at an example. A cyclist slows along astraight line from 5.5 m/s to 1.0 m/s in 3.0 s. What is theaverage acceleration of the cyclist?Step 1: List the given and unknownvalues.Unknown:acceleration, aGiven:initial speed,vi 5.5 m/sfinal speed,vf 1.0 m/sStep 2: Write the equation.Step 3: Insert the known values andsolve for the unknown value.time, t 3.0 svf – vi v a ttMath Skills6. Calculate A turtleswimming in a straight linetoward shore has a speedof 0.50 m/s. After 4.0 s, itsspeed is 0.80 m/s. What isits average acceleration?Show your work.m/s – 5.5 m/sa 1.03.0 s–4.5m/sa 3.0 sa –1.5 m/s2So, the cyclist accelerated at –1.5 m/s2. The acceleration was negative because the cyclist was slowing down.Her initial, or starting, speed was higher than her finalspeed.Copyright by Holt, Rinehart and Winston. All rights reserved.Interactive Reader239Motion
NameSECTION 2ClassDateAcceleration continuedHow Can You Graph Accelerated Motion?READING CHECK7. Define What is constantacceleration?Remember that you can determine the speed of anobject by examining a graph of distance versus time.Similarly, you can determine an object’s acceleration byexamining a graph of speed versus time.A straight line on a graph of speed versus time indicates a constant acceleration. Constant acceleration isacceleration that does not change with time. The slope of astraight line on a graph of speed versus time is equal to anobject’s acceleration. A line with a positive slope indicatesthat the object is speeding up. A line with a negative slopeindicates that the object is slowing down. Let’s look at anexample of how to graph accelerated motion.Imagine a bus traveling on a straight road at 20 m/s.For the first 20 s, the bus slows to a stop at a constantrate. The bus stays stopped for 20 s. For the next 10 s,the bus accelerates at 1.5 m/s2. For the last 10 s, the buscontinues at a constant speed. Graph the speed of the busversus time from 0 s to 60 s. What is the bus’s acceleration from 0 s to 20 s? What is its final speed?Step 1: Determine the x-axis and y-axis of the graph.Here, the x-axis is time (t) in seconds and the y-axis isspeed (v) in meters per second.Graphing Skills8. Explain Why shouldyou use a horizontal line toindicate where the bus is notaccelerating?Step 2: Starting from the origin, graph each part of themotion. (The graph is shown at the top of the next page.)A. The bus began at t 0 s and v 20 m/s. It slowed witha constant acceleration to t 20 s and v 0 m/s.Draw a straight line connecting these two points.B. From 20 s to 40 s, the bus’s speed was 0 m/s. Draw ahorizontal line at v 0 m/s from t 20 s to t 40 s.C. From 40 s to 50 s, the bus accelerated at 1.5 m/s2.Draw a line from t 40 s and v 0 m/s with a slope of1.5 m/s2. End the line at t 50 s.D. From 50 s to 60 s, the bus’s speed was constant. Drawa horizontal line from t 50 s to t 60 s at v 15 m/s.Step 3: Read the graph to determine the bus’s acceleration and final speed. The acceleration between 0 s and20 s is equal to the slope of the line between these twopoints. Therefore, the acceleration was –1 m/s2. From thegraph, you know that the bus was traveling 15 m/s att 50 s. Therefore, the bus’s final speed was 15 m/s.Copyright by Holt, Rinehart and Winston. All rights reserved.Interactive Reader240Motion
NameClassDateAcceleration continuedSECTION 2Speed vs. Time2520Speed (m/s)D15CA10Graphing Skills5B00102030405060Time (s)The slope of this part of the graphis –1 m/s2. Therefore, the bus’sacceleration during this time periodwas –1 m/s2. Because the bus’s acceleration was constant, this part ofthe graph is a straight line.From 40 s to 50 s, the bus accelerated at 1.5 m/s2. Therefore, its speedincreased by (1.5 m/s2) (10 s) 15 m/s. Since its starting speed was0 m/s, its final speed was 15 m/s.9. Apply ConceptsSuppose the bus acceleratedat 1.0 m/s2 from 40 s to 50 s.Draw a line showing thisacceleration.10. Calculate What wouldbe the bus’s speed at 50 sif the bus accelerated at1.0 m/s2 from 40 s to 50 s?DETERMINING ACCELERATION FROM DISTANCE VERSUSTIME GRAPHSYou’ve just seen that you can determine whether anobject is accelerating by examining a graph of speedversus time. You can also identify acceleration by examining a graph of distance versus time. On a graph ofdistance versus time, a curved line indicates acceleration.For example, compare the two graphs in the figure below.They show the motion of a bicyclist in a race.4QFFE N T4QFFE WT 5JNF 5JNF T On a speed versus time graph, thebicyclist’s motion is a straight linewith a negative slope. Therefore, thebicyclist was slowing down with aconstant acceleration.Distance (m)Distance vs. Time25201510500123Time (s)45EHHDBG@ EHL K 11. Explain Is the bicyclistspeeding up or slowingdown? Explain your answer.On a distance versus time graph, thebicyclist’s motion is a curved line.The curve of the line indicates thatthe bicyclist was accelerating.Copyright by Holt, Rinehart and Winston. All rights reserved.Interactive Reader241Motion
NameClassDateSection 2 ReviewSECTION VOCABULARYacceleration the rate at which velocity changesover time; an object accelerates if its speed,direction, or both change1. Explain Why is a fan blade spinning at a constant speed constantly accelerating?2. Graph The graph below shows speed versus time for a car traveling in a straightline. From 40 s to 50 s, the car accelerated at a constant rate of 1 m/s2. Completethe graph to show this information.Speed vs. Time for a Moving Car1098Speed (m/s)7654321005101520253035404550Time (s)3. Interpret Based on the graph above, what is the car’s acceleration between 25 sand 30 s? Explain your answer.4. Calculate Based on the graph above, what is the car’s acceleration between 10 sand 25 s? Explain your answer.Copyright by Holt, Rinehart and Winston. All rights reserved.Interactive Reader242Motion
Feb 14, 2014 · speed as time increases? KEY IDEAS SECTION2 Acceleration Motion This cyclist’s speed increases by 1 m/s every second. Therefore, his acceleration is 1 m/s/s, or 1 m/s2. 1 m/s 1:0000 2:0000 3:0000 4:0000 5:0000 2 m/s 5 m/s 3 m/s 4 m/s CHAPTER 11
Centripetal Acceleration" The acceleration of an object moving in a circular path and at constant speed is due to a change in direction." An acceleration of this nature is called a centripetal acceleration. CENTRIPETAL ACCELERATION ac vt 2 r centripetal acceleration (tangential speed)2 radius of circular path Section 1 Circular Motion
3.1 Which of the following statements correctly defines acceleration? Question 1 A. Acceleration is the rate of change of displacement of an object. B. Acceleration is the rate of change of velocity of an object. C. Acceleration is the amount of distance covered in unit time. D. Acceleration is the rate of change of speed of an object. Section .
(b) The centripetal acceleration is half as large because centripetal acceleration depends on the inverse of the radius: 1 2 a c v2 2r. (c) The centripetal acceleration is four times as great because centripetal acceleration depends on the square of the speed: 4a c (2v)2 r. 2.
Section 1 Acceleration: Practice Problems Use the v-t graph of the toy train in )LJXUH to answer these questions. a. When is the train ¶s speed constant? b. During which time interval is the train ¶s acceleration positive? c. When is the train ¶s acceleration most negative? 62/87,21 D WR V b. 0.0 to 5.0 s c. 15.0 to 20.0 s 16:(5
Chapter: Motion, Acceleration, and Forces Table of Contents Section 3: Motion and Forces . also are accelerated. Acceleration This acceleration makes them feel as if a . Sometimes it is obvious that a force has been applied. 3 Motion and Forces But other forces arenÕt as noticeable. Changing Motion
Two common problems 1. Acceleration and velocity are always in the same direction a. No, as an object is thrown upward, velocity is y, acceleration is –y 2. Acceleration is zero at the highest point. a. No, at the highest point, the velocity is zero, but acceleration is always - 9.80m/s2 b. The object changes velocity, it must have an .
max r 1 s 2g(m 2r 2 m 1r 1) m 1r2 1 m 2r22 3:05 r 2 9:81(58 0:15 0:130 3:05) 0:130 3:052 58 0:152 24:55 m s b) The overall acceleration is changing direction throughout the motion. Vector acceleration is thus not constant. c) and d) Neither tangential acceleration nor angular acceleration are constant. First of all, the two are .
Acceleration (m/s2) Force, calculated (N) Analysis Questions 1. If the centripetal acceleration experienced by a mass undergoing uniform circular motion is v2/r, calculate the centripetal acceleration experienced by the rotating mass in this experiment for each speed. Record the results in Table 1. 2. What direction is the acceleration?
