Honors Physics Unit 03 - CAPM Constant Acceleration Particle Model ‘The front of each model packet should serve as a storehouse for things you'll want to be able to quickly look up later. We will usually try to give you some direction on a useful way to organize this space (see the table below). CAPM Model Summary 1 adapted from Modeling Workshop Project © 2006Worksheet 1: Speeding Up, Slowing Down or Constant Velocity? Below are a series of motion diagrams. Each one shows the location of the object each time the clock ticks one second. In each motion diagram, the object is either traveling with a constant velocity, speeding up or slowing down. The object is also moving in either the positive or negative direction. For each one, choose the best description of the object's motion and its direction of travel. Be sure to explain how you made your choice by referring to aspects of the motion diagram. a1. e-e-e-e-e- a 4 3 2 A ° 1 2 3 4 meters Circle one: Constant Velocity Speeding Up Slowing Down Circle one: _ Moving in the positive direction Moving in the negative direction Explain your choice: ° 1 2 3 4 5 6 7 8 meters Circle one: Constant Velocity Speeding Up Slowing Down Circle one: _ Moving in the positive direction Moving in the negative direction Explain your choice:#3. 3 7 6 5 4 3 2 A 0 meters Circle one: Constant Velocity Speeding Up Slowing Down Circle one: Moving in the positive direction Moving in the negative direction Explain your choice: 4, ° 1 2 3 4 5 6 7 8 meters Circle one: Constant Velocity Speeding Up Slowing Down Circle one: Moving in the positive direction Moving in the negative direction Explain your choice:45. te0s 0 1 2 3 4 5 6 7 8 meters Circleone: Constant Velocity Speeding Up Slowing Down Circle one: _ Moving in the positive direction Moving in the negative direction Explain your choice: 4 3 2 a ° 1 2 3 4 meters Circle one: Constant Velocity Speeding Up Slowing Down Circle one: Movingin the positive direction Moving in the negative direction Explain your choice:47, eo— oe e- e @® ee 4 3 2 A o 1 2 3 4 meters Circle one: Constant Velocity Speeding Up Slowing Down Circle one: Moving in the positive direction Moving in the negative direction Explain your choice: #8. t=08 oe es e*- e- e ° 1 2 3 4 5 6 7 8 meters Circleone: Constant Velocity Speeding Up Slowing Down Circle one: Moving in the positive direction Moving in the negative direction Explain your chWorksheet 2: Changing Velocities Below is a motion diagram for an object that is speeding up. The positions and the velocity vectors are drawn to scale. A table of data is provided for you to compare with the motion diagram. [Clock Reading (seconds) Position (meters) Velocity (meters/second) 0 0.00 0.0 1 0.25) 05: 2 1.00 1.0 3 2.13 15 4 4.00 2.0 ttt tot 11> oo 0S 10.8 20 2508s e@ o> e——_> e—____> e—____> Difference in velocity vectors #1. For this motion, we can see that the velocity is changing. Is the magnitude of the velocity increasing or decreasing? How do you know? Refer to a visual clue on the motion diagram in your explanation. Now, we want to look at how the velocity is changing for this object. How much is the velocity changing each second? To do this, we're going to need to determine the difference between the velocity at two different clock readings. Start by measuring the length of the velocity vector for the object at 1 second. Next, measure the length of the velocity vector at 2 seconds. In the space below the motion diagram, draw a vector that is the difference between the two you just measured. Another way to look at this is to figure out what vector must be added to the t = 1 s vector to get the t= 2s vector. This new vector represents the change in the velocity during a time interval of one second. It’s how much the velocity has changed from t = 1s to t = 2s. For now, let's call this the change in velocity from one to two seconds.Let’s look at the change in velocity between other consecutive clock readings. In the space below, do the same thing for the velocity at t = 3 s and t = 2s. Start by measuring the length of the velocity vector for the object at 2 seconds (Hint: You already know this if you wrote it down previously). Next, measure the length of the velocity vector at 3 seconds. In the space below the motion diagram, draw a vector that is the difference between the two you just measured. #2. How does the change in velocity from two to three seconds compare in magnitude to the change in velocity from one to two seconds (from the problem above]? How does it compare in direction? Repeat the same process for one other consecutive set of clock readings such as 0 1 seconds or 3-4 seconds. #3, How does the change in velocity for your consecutive clock readings compare in magnitude to the change in velocity from the previous two examples? How does it compare in direction? #4, From your analysis, would you say that the change in velocity for each one second time interval is constant or changing? Explain how you made your choice. #5. What does it mean to have a constant change in velocity for each one second time interval? How would an object be moving if its change in velocity for each one second time interval is constant?Let’s consider the motion of a second object. Below is a motion diagram (drawn to the same scale) as well as a data table to compare. Using the same technique that you used in the first. part, determine the change in velocity for each one second time interval for three time intervals of your choice (e.g. 0-1 second, 1~2 second, etc,). Clock Reading (seconds) Position (meters) Velocity (meters/second) 0 0.00 0.00 1 0.13 0.25 2 0.50 0.50 3 1.13 0.75 4 2.00 1.00 1 1 L |» T 09 «05 1015 20 8S 40a eer o> e—_ > e—> Difference in velocity vectors intervals compare in magnitude to each #6, How do the changes in velocity for the three other? How do they compare in direction? #7. From your analysis, would you say that the change in velocity for each one second time interval is constant or changing? Explain how you made your choice. #8. How does the change in velocity for each one second time interval for this object compare with the change in velocity for each one second time interval for the first object?#9, What does it mean if one objects has a smaller (or larger) change in velocity for each one second time interval from a second object? #10. What does it mean if an object has a change in velocity for each one second time interval that is equal to zero? At this point, we should come up with a name for the change in velocity for each one second time interval, as it seems like an important concept for understanding motion. We will call it the acceleration of the object.Uniformly Accelerated Particle Model Lab Extension: Increasing and Decreasing Speed 1. Increasing speed in the positive direction ‘a. Without using the motion detector, observe the motion of the cart as it starts from rest and rolls down the incline. _—_ ty ’. Draw a motion map of the cart’s motion along the ramp. Include velocity and acceleration’ vectors. + . Is the velocity positive or negative? d. Is the acceleration positive or negative? «, Predict the graphs describing | f Record the graphs as displayed the motion. by the motion detector. g. The slope of the +f + position-time graph is (Constant / increasing / decreasing) 5 § and 2 2 (positive / negative) 2 g and represents 0 >| 0 > = ft t +f +h h. The slope of the velocity-time graph is 2 > (constant increasing / decreasing) 80 7 | 80 zr and 3 3 (positive / negative) and represents YY y 4 4 gt st g ie 50 >| 50| > 3 tls 7 3 3 3. 8. y ¥ ©Modeling Instruction 2013 1 U3 Uniform Acceleration — lab extension v3.12. Decreasing speed in the positive direction @. Without using the motion detector, observe the motion of the cart slowing after an initial push. Answer the following questions for the cart while coasting Stop the cart at <5) Give the cart an initial push up the ramp. _ its highest point. 3) rt id : cal —— + 3 ee = ; nee 0 position —— . Draw a motion map of the cart’s motion along the ramp. Include both velocity and + 0 acceleration vectors. ¢.Is the velocity positive or negative? d. Is the acceleration positive or negative? , Predict the graphs describing | & Record the graphs as displayed the motion, by the motion detector. +R +5 g, The slope of the position-time graph is < “ (constant /inereasing / decreasing) 8 g and 3 z (positive / negative) & 2 and represents 0 7 0 z + + h. The slope of the velocity-time graph is 2 2 (constant increasing / decreasing) 3° 7 | 3° and 2 2 (positive / negative) and represents YY Y ’ i. s* & 8 2 50 > | Bo > 2 Pole t s 8 ©Modeling Instruction 2013 2 U3 Uniform Acceleration ~ lab extension v3.13. Increasing speed in the negative direction ‘a, Observe the motion of the cart starting from rest and rolling down the incline without using the motion detector. Se) e3 a _ 0 position _—_—— . Draw a motion map of the cart’s motion along the ramp. Include both velocity and 7 0 acceleration vectors. ¢. Is the velocity positive or negative? . Is the acceleration positive or negative? e. Predict the graphs desoribing the | £ Record the graphs as displayed motion. by the motion detector. g. The slope of the position-time graph is (constant / increasing / decreasing) and (positive / negative) ‘and represents +h +4 position position © Y if t bh, The slope of the velocity-time graph is (constant / increasing / decreasing) > and ‘(positive / negative) and represents + + velocity S + velocity < < > sf acceleration S Y acceleration S ¥ I< ©Modeling Instruction 2013 3 U3 Uniform Acceleration ~ lab extension v3.14. Decreasing speed in the negative direction '& Observe the motion of the cart slowing after an inital push without using the motion detector. Answer the following questions for the cart while coasting. Stop the cart at its highest point. Give the cart an initial push up the ramp. eat) =] b, Draw a motion map of the carts motion along the ramp, Include both velocity and acceleration vectors. c.Is the velocity positive or negative? 4. Is the acceleration positive or negative? @, Predict the graphs describing ] & Record the graphs as displayed the motion. by the motion detector. . The slope of the +e +4 position-time graph is (constant / increasing / decreasing) § 5 and 2 2 (positive / negative) 3 g and represents 0 >| 0 > t t ft h, The slope of the velocity-time graph is 2 2 (Constant / inereasing / decreasing) 80 80 > and g g © (positive / negative) e e and represents -| - 4 ‘ gt gt s s 50 7? | 20 -| 3. ©Modeling Instruction 2013 4 US Uniform Acceleration ~ lab extension v3.15. Up and down the ramp ‘a. Observe the motion of the cart after an initial push without using the motion detector. Answer the following questions for the cart while coasting, Give the cart an initial push up the ramp. fey) _____—— SS Carich the cart just before it reaches the motion detector on the way back down. O position _—___— B. Draw a motion map of the cart’s motion along the ramp. Include both velocity and acceleration vectors. + 0 c.Is the velocity positive or negative? 4. Is the acceleration positive or negative? Does the direction of the velocity change? Does the direction of the acceleration change? ®. Predict the graphs describing | f Record the graphs as displayed the motion. by the motion detector. g. Describe how the slope ’ ‘ ow + + of the position-time graph 5 5 changes: 0 —> > t ° t ft 4h h. Describe the slope of the ocity-t > > velocity-time graph: 3 >| 3 > . 7 t 2 9 t 8 2 oY ¥ ‘ 4 gt s+ § § £ = 50 7 | 20 rv “y (©Modeling Instruction 2013 6 US Uniform Acceleration — lab extension v3.16. Up and down the ramp & Observe the motion of the cart after an initial push without using the motion detector. Answer the following questions for the cart while coasting. ee Stop the cart at ES its tighest point, Give the cart an initial push up the ramp 0 position [cart] +] | , Draw a motion map of the cart's motion along the ramp. Include both velocity and acceleration vectors. f+ ++} + ¢. Is the velocity positive or negative? d. Is the acceleration positive or negative? Does the direction of the velocity change? Does the direction of the acceleration change? c, Predict the graphs describing] £ Record the graphs as displayed the motion. by the motion detector. A i g, Describe how the slope + + of the position-time graph © = changes § g 30 > | 30 S t 3 & a eo >< >< h. Describe the slope of the 2 > velocity-time graph: 3 0 3 0 2 2 oy vy 4 4 + + 5 § sf Ss §o-—_—____> | §o -————_-> 3 3 8. a. l< l< ‘©Modeling Instruction 2013 1 US Uniform Acceleration — lab extension v3.1Honors Physics Unit 03 - CAPM. Worksheet 3: Graphical Interpretation ‘Match the numbered scenarios below with a graph from the set of eight directly above them. Some graphs x | may be used more than once. * D 4. | | o \ | aN cr n A (1) A marble is rolled at constant speed along a horizontal surface toward the origin. The marble is released ata distance of 1 meter away from the origin. (2) Ablock sits at rest ona table 1 meter above the floor. Take the origin to be the level ofthe loa. (3) Aba is dropped from a height of 2 meters above the floor. Take the origin to be the point from which the ball is released. (4) Aball is rolled along a horizontal surface. The ball strikes a wall and rebounds toward the origin. (5) A aris parked on asteep bill, Me v, A B . t i Lg F 0 t 0 t (1) A block is dropped from rest with a height of 1 meter above the floor. Take the origin to be at the level ofthe floor. (2) A marbles released from the top of an inclined plane. Assume that positive x is measured down the plane. (3) A balls thrown straight up into the air. Take the origin to be at the level ofthe floor. (4) Aball ros along a horizontal surface without changing speed. The ball strikes a wall and rebounds toward the origin at approximately the same speed as before, (5) Amarble rolls on to a piece of felt, eventually stopping. 0 s Le x 1 adapted from Modeling Workshop Project © 2006Worksheet 4: Stacks of Kinematic Graphs Given the following position vs time graphs, construct the corresponding velocity vs time and acceleration vs time graphs, create velocity and acceleration motion maps and describe the motion. If you see a dashed line in a graph it tells you the motion changes at that time. position velocity + + acceleration vel: ace: Description: position + > velocity +t 5 S 2 e._____?7 2 time 8 3 s + vel: Om — = ace: Description: ‘©Modeling Instruction - AMTA 2013 U3 Uniform acceleration - ws 3 v3.1position time time + +t 7 5 g 3 & & |}——____+——_> a time 3 time 8 8 & o + a vel: vel: Om om yo ey }—_+}+_++_+}+—> oto * ace: ace: Description: Descriptions ©Modeling Instruction - AMTA 2013 2 U3 Uniform acceleration - ws 3 v3.1‘time pon" + uoHee|e00e + wopeseje29e ed Om vel: ace: Om vel: acc: i e & U3 Uniform acceleration - ws 3 v3.1 ©Modeling Instruction - AMTA 2013uonisod time + Aysojea +s UORRIB|OD0e time time > + Hipopan “5 opeuajooae > vel: Om om 8 8 ion: Descripti Description: UB Uniform acceleration - ws 3 v3.1 (©Modeling Instruction - AMTA 2013Honors Physics Unito3- CAPM Worksheet 5: Graphs of Motion with Changing Velocity #1, Consider the velocity-vs-time graphs and describe the motion of the objects. Object A Object B 16, 16 2 v(m/s) v (m/s) - “4 a “8 “8 8 ts) 1) a) Describe the motion in words. ) Sketch a motion diagram. Be sure to include both velocity and acceleration vectors. 6) Determine the displacement between 4 and 8 seconds. Show work! 4) Determine the average acceleration during the first 3 seconds. Show work! 1 adapted from Modeling Workshop Project © 2006Honors Physics Unit03- CAPM #2, Use the velocity-vs-time graph to analyze the motion of the object. a. Give a written description of the motion. 8 6 4 y2 (mis) 0 b. Sketch a motion map. Be sure to include both 2 velocity and acceleration vectors. 4 6 68 c. Determine the displacement of the object from t= 0s to t= d. Determine the displacement of the object from t= 4s to t= 8s. e, Determine the displacement of the object from ¢= 2 sto t= 6s. £, Determine the object's acceleration at t= 4s, #3. Sketch a possible position-vs-time graph for the motion of the object. Explain why your graph is only one of many possible graphs. 2. from Modeling Workshop Project © 2006Worksheet 6: Quantitative Acceleration Problems 1. A poorly tuned car accelerates from rest to a speed of 28 m/s in 20s a, Make a well-labeled diagram of the situation. b. Make a well-labeled graphical representation of the situation. . List given quantities and quantities to find as you determine: i. What is the average acceleration of the car? ii, How far does it travel in this time? velocity (m/s) time (s) 2. Att = 0's a car has a speed of 30 m/s. After 6s, its speed is 15 m/s. a. Make a well-labeled diagram of the situation b. Make a well-labeled graphical representation of the situation, c. List given quantities and quantities to find as you determine: i, What is the average acceleration of the car? ii, How far does it travel in this time? velocity (m/s) time (s) ©Modeling Instruction - AMTA 2013 1 U3 Uniform Acceleration - ws 5v3.03. Astudent drops a rock from the top of a 30 meter tall building. a. Make a well-labeled diagram of the situation. b. Make a well-labeled graphical representation of the situation. c. List given quantities and quantities to find as you determine how fast the rock will be traveling just before impact. time (s) 4, Abus initially moving at 20 m/s slows by 4 m/s each second. a. Make a well-labeled diagram of the situation, b. Make a well-labeled graphical representation of the situation. c. List given quantities and quantities to find as you determine: i. How much time does it take the bus to stop? ji, How far does it travel while braking? velocity (mis) time (s) ‘©Modeling Instruction - AMTA 2013 2 U3 Uniform Acceleration ~ ws 5v3.05. A car whose initial speed is 30 m/s slows uniformly to 10 m/s in 5 seconds. a, Make a well-labeled diagram of the situation. b. Make a well-labeled graphical representation of the situation. c. Uist given quantities and quantities to find. i. Determine the acceleration of the car. ii, Determine the distance the car travels in the 3rd second (from t = 2s tot = 3s) velocity (m/s) 6. A dog runs down his driveway with an initial speed of 5 m/s for 8 s, then uniformly increases his speed to 10 m/s in 5s. a, Make a well-labeled diagram of the situation, b. Make a well-labeled graphical representation of the situation, c. List given quantities and quantities to find as you determine: What was the dog’s acceleration during the 2° part of the motion? |. How long is the driveway? velocity (mis) time (8) ‘©Modeling Instruction - AMTA 2013 3 U3 Uniform Acceleration - ws 5v3.07. A physics student skis down a slope, with a constant acceleration of 2.0 m/s” for 15 seconds. a. Make a well-labeled diagram of the situation. b, Make a well-labeled graphical representation of the situation. . List given quantities and quantities to find as you determine the length of the slope. velocity (m/s) 8. Amountain goat starts a rock slide and the rocks crash down the slope 100 m in five seconds. a. Make a well-labeled diagram of the situation. b, Make a well-labeled graphical representation of the situation. ies and quantities to find as you determine the acceleration of the rocks. . List given quant velocity (m/s) time (5) ©Modeling Instruction - AMTA 2013 4 U3 Uniform Acceleration - ws $v3.0