Name: Period: Unit I: Motion Subunit B: Constant Acceleration Chapter 2 Sections 2 and 3 Texas Physics p. 47-63 Equations (figure 2.6 p.56) Variables, Units (ch 2 Summary p.72) Method for problem solving G: U: E: S: S: NOTES:
Unit I-B Objectives What you should know when all is said and done 1. Given a x vs. t graph, you should be able to: a. describe the motion of the object (starting position, direction of motion, velocity) b. draw the corresponding v vs. t graph c. draw the corresponding a vs. t graph d. determine the instantaneous velocity of the object at a given time 2. Given a v vs. t graph, you should be able to: a. describe the motion of the object (direction of motion, acceleration) b. draw the corresponding x vs. t graph c. draw the corresponding a vs. t graph d. write a mathematical model to describe the motion e. determine the acceleration f. determine the displacement for a given time interval 3. You should be able to determine the instantaneous velocity of an object in three ways: a. determining the slope of the tangent to an x vs. t graph at a given point. b. using the mathematical model v f = aδt + v i c. using the mathematical model v f 2 = v i 2 + 2aΔx 4. You should be able to determine the displacement of an object in three ways: a. finding the area under a v vs. t curve b. using the mathematical model Δx = ½ aδt 2 + v i Δt c. using the mathematical model v f 2 = v i 2 + 2aΔx 5. You should be able to determine the acceleration of an object in five ways: a. finding the slope of a v vs. t graph b. using the mathematical model a = Δv/Δt c. rearranging the mathematical model Δx = ½ aδt 2 + v i Δt d. rearranging the mathematical model v f = aδt + v i e. rearranging the mathematical model v f 2 = v i 2 + 2aΔx
Unit 1B Reading/Notes In the opening lab, the motion of an object rolling down an inclined ramp was investigated. We did not concern ourselves with the rotational motion of the object and instead imagined it as a point particle. By recording the position of the particle at equal time intervals, a position vs. time graph was generated. The shape of the graph appeared to be a top opening parabola. In the constant velocity model, we established that the slope of the position-time graph (change in position divided by change in time) is the average velocity during the time interval. The slope of a straight line can be taken at any two points on the line because the slope is constant. So what does the fact that the slope is not constant in our new experiment mean? A changing slope on a position vs. time graph tells me that: The average velocity can also be found for a curved position-time graph by the same method as for a linear graph, by taking the total change in position over a time interval. However, on a curved graph, the slope is constantly changing at each point, so the average velocity often isn t a very good description of the object s motion. In order to find the velocity of the object at any given instant, or the instantaneous velocity, a line can be drawn through two points to first find the average velocity. The slope of this line will be approximately equal to the instantaneous velocity at some point exactly halfway in between these two points. (An average is also like taking the two instantaneous velocities, adding them together and dividing by two: v ave = (v i + v f )/2.) x x x!t!x t!t!x t!t!x t The closer the two points are on the curve, the closer the average velocity will be to the instantaneous velocity. As the two points get closer and closer, they reach a point where they meet and the line going between them is now tangent to the line at that point. A tangent line touches a curve at just one point without crossing from one side of the curve to the other. The slope of the tangent tells us the velocity at the time corresponding to the point on the graph to which the tangent is drawn. Since the velocity is always changing, what we find is the instantaneous velocity. Your math teacher may have taught you how to find the equation for a parabola, but here nstruct in at physics, least five tangen we are going to use a concept called linearization to simplify the analysis of a graph by recognizing a pattern and creating a test plot that represents what model we expect the data to follow. You may know that a parabola is a graph that can also be called a quadratic function, or is represented by an equation of y vs. x 2. If we make a test-plot of position vs. time squared using our lab data, we will find that the graph becomes linear; this means we can write the equation of the new test plot in the form y = mx + b using position as the y variable and time squared as the x. Therefore we can state that the relationship between the variables was that position is directly proportional to time squared. Let s try it! x Δt t Δx
Finding instantaneous velocity by determining the slopes of tangents will allow us to create a plot of velocity vs. time. Making a graph of instantaneous velocity vs. time yields a linear graph. A linear graph (constant slope) of velocity vs. time tells me that: v Δv Δt t The slope of the velocity vs. time graph is the change in velocity divided by change in time. It tells us how much the velocity changes during each time interval. A large slope means that the velocity changes a lot every second, whereas a small slope means that the velocity changes a small amount each second. Since the rate of change in velocity is a useful idea, we give it a name: acceleration. Because both speeding up AND slowing down represent changes in velocity, they are both called acceleration (no need for the odd term deceleration ). Acceleration: Plotting the instantaneous velocity by determining the slopes of tangents will always work as long as the acceleration is constant, but it is often a bit tedious (ok, a lot tedious!). So remember: When the average velocity is determined for a time interval, we find that this average velocity is identical to the instantaneous velocity at the time in the middle of the interval. For example, if the average velocity from t = 2s to t = 4s is 10 m/s, the instantaneous velocity is 10 m/s at the time in the middle of the interval, t = 3s. Let s test this technique out on worksheet 1 to help us determine what the slope from our new linearized graph represents!
Unit I-B: Constant Acceleration Worksheet 1 t (s) x (cm) 0.0 0.0 1.0 5.0 t 2 (s 2 ) Δt (s) Δx (cm) v ave (m/s) t mp (s) The data to the left are for a marble rolling from rest down an incline. Use the positiontime data given in the data table to do the following: 2.0 20.0 3.0 45.0 4.0 80.0 5.0 125.0 A) Plot a position vs. time graph for the data on the axes below, using the entire graph area. Label the graph clearly. B) Complete the rest of the data table. For the four columns on the right, you are calculating the change from the previous row to the subsequent row. t mp means the mid-point time of the interval. 6.0 180.0 Position (cm) 0 1 2 3 4 5 6 7 8
C) Graph and label a test plot (to linearize the data) on the grid, then write the equation of the line below. D) Plot and label a velocity vs. time graph on the second grid. Be sure to plot the time column that makes your v vs. t graph an instantaneous velocity vs. time graph. Write the equation of the line below. g. Answer the 11 questions on the following page!
1. What is the meaning of the slope of a position vs. time graph? 2. What is happening to the slope of your position vs. time graph as time goes on? 3. Explain what your answers to questions 1 and 2 tell you about the motion of the marble. 4. What is the meaning of the slope of your velocity vs. time graph? Explain! 5. Compare the slope of your velocity vs. time graph to the slope of your position vs. time 2 graph. What does this tell you about the slope of your position vs. time 2 graph? 6. Write an equation that relates velocity and time for the ball using the mathematical analysis of your velocity vs. time graph. 7. Write an equation that relates position and time for the ball using the mathematical analysis of your position vs. time 2 graph. 8. On the position vs. time graph, draw a line which connects the data point at t = 0 to the data point at t = 6 s and calculate the slope of this line. Explain what the slope of this line tells you about the motion of the ball. 9. On the position vs. time graph, draw a line which connects the data point at t = 2 s to the data point at t = 4 s. Calculate the slope of this line. Explain what the slope of this line tells you about the motion of the ball. 10. On the position vs. time graph, draw a line tangent to the graph at t = 3 s. Calculate the slope of this line. Explain what the slope of this line tells you about the motion of the ball. 11. Compare the slopes you have calculated in questions 8, 9, and 10. Explain the results of your comparison.
Unit I-B: Constant Acceleration Worksheet 2 1. Accelerating objects are objects that are changing their velocity. Name the three controls on an automobile that cause it to accelerate. 2. An object must be accelerating if it is moving. Circle all that apply. A) with changing speed D) in a circle B) extremely fast E) downward C) with constant velocity F) none of these 3. If an object is NOT accelerating, then one knows for sure that it is A) at rest C) slowing down B) moving with a constant speed D) maintaining a constant velocity 4. An object with an acceleration of 10 m/s 2 will. Circle all that apply. A) move 10 meters in 1 second C) move 100 meters in 10 seconds B) change its velocity by 10 m/s in 1 s D) have a velocity of 100 m/s after 10 s 5. Ima Speedin puts the pedal to the metal in her Porsche and accelerates from 0 to 60 mi/hr in 4 seconds. Her acceleration is A) 60 mi/hr C) 15 mi/hr/s B) 15 m/s/s D) -15 mi/hr/s 6. A car speeds up from rest to +16 m/s in 4 s. Calculate the acceleration. 7. A car slows down from +32 m/s to +8 m/s in 4 s. Calculate the acceleration. 8. Read the following statements and indicate the direction (up, down, east, west, north or south) of the acceleration vector. Dir'n of Description of Motion Acceleration a. A car is moving eastward along Lake Avenue and increasing its speed from 25 mph to 45 mph. b. A northbound car skids to a stop to avoid a reckless driver. c. An Olympic diver slows down after splashing into the water. d. A southward-bound free quick delivered by the opposing team is slowed down and stopped by the goalie. e. A downward falling parachutists pulls the chord and rapidly slows down. f. A rightward-moving Hot Wheels car slows to a stop. g. A falling bungee-jumper slows down as she nears the concrete sidewalk below.
10. The motion of several objects is depicted on the position vs. time graph. Answer the following questions. Each question may have less than one, one, or more than one answer. A) Which object(s) is(are) at rest? B) Which object(s) is(are) accelerating? C) Which object(s) is(are) not moving? D) Which object(s) change(s) its direction? E) Which object is traveling fastest? F) Which moving object is traveling slowest? G) Which object(s) is(are) moving in the same direction as object B? 4. The motion of several objects is depicted by a velocity vs. time graph. Answer the following The motion of several objects is depicted by a velocity vs. time graph. Answer the following questions. questions. Each question may have less than one, one, or more than one answer. Each question may have less than one, one, or more than one answer. a. Which object(s) is(are) at rest? A) Which object(s) is(are) at rest? b. Which object(s) is(are) accelerating? B) Which object(s) is(are) accelerating? c. Which object(s) is(are) not moving? C) Which object(s) is(are) not moving? d. Which object(s) change(s) its direction? D) Which object(s) change(s) its direction? e. Which accelerating object has the smallest acceleration? E) Which accelerating object has the smallest acceleration? f. Which object has the greatest acceleration? F) Which object has the greatest acceleration? g. G) Which Which object(s) object(s) is(are) is(are) moving moving in in the the same same direction direction as as object object E? E?
Unit I-B: Constant Acceleration Worksheet 3 MOP Connection: Kinematic Graphing: sublevels 1-11 (emphasis on sublevels 9-11) hysics Classroom: /1DKin/1KinTOC.html Graphing Summary Constant Velocity Constant Velocity Constant + A (emphasis e 1-D Kinematics on If sublevels chapter the object 9-11) at The Physics Classroom: Constant + Acceleration Constant - Acceleration Constant - is speeding up, the Motion acceleration Object is in the same direction as the velocity (adding to the ww.physicsclassroom.com/class/1dkin/1kintoc.html Object in moves moves One Dimension in + Direction Object moves in - Direction Object moves in - Direction Object moves in Direction Object moves speed). If the object is slowing down, the acceleration is in the opposite direction of the velocity y (taking Constant away + from Acceleration the speed). 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MOP Connection: Kinematic Graphing: sublevels 1-11 (emphasis on sublevels 9-11) hysics Classroom: e 1-D Kinematics chapter at The Physics Classroom: Constant + Acceleration Constant - Acceleration Constant - A /1DKin/1KinTOC.html ww.physicsclassroom.com/class/1dkin/1kintoc.html Object Constant moves in Velocity - Direction Object Constant moves in Velocity - Direction Object Constant moves + A (emphasis on sublevels 9-11) Object moves in + Direction Object moves in - Direction Object moves ematic Graphing: Velocity sublevels Dir'n: 1-11 + (emphasis or - on sublevels Velocity 9-11) Dir'n: + or - Velocity Dir'n: + or - Velocity Dir'n y Speeding Constant up or + Acceleration Slowing Down? Speeding Velocity up Dir'n: or Slowing + or Down? - Speeding Velocity up Dir'n: or Slowing + or Down? - Speeding Velocity up Dir'n or ection B) Object Moving Constant moves in Velocity the in + Direction direction and slowing Constant down + Acceleration Speeding up or ion Object moves in - Direction Object moves in + Direction or - Velocity Dir'n: + or - - Velocity Dir'n: + or - Velocity Dir'n: + or - Speeding up or Slowing Down? Speeding up or Slowing Down? Graphing Summary Constant + Acceleration tion Constant - Acceleration Object moves in - Direction ection Object moves in + Direction e 1-D Kinematics chapter at The Physics Classroom: or ww.physicsclassroom.com/class/1dkin/1kintoc.html n - Constant Velocity - Dir'n: Acceleration + or - Constant Velocity - Dir'n: Acceleration + or - ion Down? Speeding Object moves up or in - Slowing Direction Down? Speeding Object moves up or in + Slowing Direction Down? ematic Graphing: sublevels 1-11 (emphasis on sublevels 9-11) - C) Velocity Moving Dir'n: in the + - direction or - and speeding Velocity Dir'n: up + or - own? ion Speeding Constant up or Slowing Velocity Down? Object moves in - Direction Speeding Constant up or + Acceleration Slowing Down? The Physics Classroom, 2009 Object moves in + Direction - Velocity Dir'n: + or - Velocity Dir'n: + or - Velocity Dir'n: + or - Velocity Dir'n: + or - Velocity Dir'n Speeding up or Study Lessons 3 and 4 of the 1-D Kinematics chapter at The Physics Classroom: Speeding up or Slowing Down? Graphing Summary http://www.physicsclassroom.com/class/1dkin/1kintoc.html Acceleration Acceleration Constant - Acceleration Object moves in - Direction Velocity Dir'n: + or - Speeding up or Slowing Down? Acceleration Constant - A Object moves Velocity Dir'n Speeding up or tion ection n ion or - - Down? own? Constant + Acceleration Constant - Acceleration Constant - Acceleration Constant Object moves - Acceleration in - Direction Object moves in + Direction Object moves in - Direction Object moves in + Direction D) Velocity Velocity Moving Dir'n: Dir'n: in the + - direction + or - Velocity Dir'n: + or - or - and slowing Velocity down Dir'n: + or - Speeding up or Slowing Down? Speeding up or Slowing Down? Speeding up or Slowing Down? Speeding up or Slowing Down? The Physics Classroom, 2009 Constant - Acceleration Object moves in - Direction Velocity Dir'n: + or - Speeding up or Slowing Down? Constant - A Object moves Velocity Dir'n Speeding up or Acceleration n ion Constant - Acceleration Page 20 Object moves in - Direction Constant - Acceleration Object moves in + Direction 2009 Page - Velocity Dir'n: + or - Velocity The Physics Dir'n: Classroom, + or - 2009 own? Speeding up or Slowing Down? Speeding up or Slowing Down?
2. While cruising along a dark stretch of highway at 25 m/s ( 55 mph), you see, at the fringes of your headlights, that a bridge has been washed out. You apply the brakes and come to a stop in 4.0s. Assume the clock starts the instant you hit the brakes. Call the initial direction positive. A) Construct a qualitative x vs. t graph of the situation described, and a quantitatively accurate v vs. t graph to describe the situation. Position (m) Velocity (m/s) B) On the v vs. t graph at right, graphically represent the car s displacement during braking. C) Utilizing the graphical representation, determine how far the car traveled during braking. (Show work!) Acceleration (m/s 2 ) D) Determine the car s acceleration, then sketch a quantitatively accurate a vs. t graph. E) Using the equation you developed for displacement of an accelerating object determine how far the car traveled during braking. (Show your work.) 0 F) Compare your answers to C and E. 14
3. Use the following graph to answer questions for an object. A) Give a written description of the motion. 12 9 v (m/s) 6 3 0-3 -6 2 4 6 8 t (s) B) Determine the displacement from t = 0s to t = 4 s. -9-12 C) Determine the displacement from t = 4 s to t = 8 s. D) Determine the average acceleration of the object s motion. v (m/s) 4. Use the following graph to answer questions for an object. A) Give a written description of the motion. 8 6 4 2 B) Determine the displacement from t = 0s to t = 4 s. 0-2 2 4 6 8 t (s) -4 C) Determine the displacement from t = 4 s to t = 8 s. -6-8 D) Determine the displacement from t = 2 s to t = 6 s. E) Determine the object s acceleration at t =4s. 52 Velocity (m/s) 5. A car accelerates from rest to a speed of 20 m/s in a time of 5.0 seconds. A) Sketch a velocity-time graph showing the motion of the car. B) What is the acceleration of the car? C) What distance will it travel as it accelerates? How do you know? 14
Unit I-B: Constant Acceleration Worksheet 4 1. The graph at right represents the motion of an object. A) Where on the graph above is the object moving most slowly? How do you know? B) Between which points is the object speeding up? How do you know? C) Between which points is the object slowing down? How do you know? D) Where on the graph above is the object changing direction? How do you know? 2. A) For each line segment shown on the graph, identify if the acceleration and velocity are positive, negative, or zero. Then decide if the object would be speeding up, slowing down, not moving, or moving with constant velocity. Fill in the chart to show your answers. (also, see figure 2.3 on p.49) Velocity (m/s) v a Description B A A C B D E F G C D E F G B) On the graph there is a dark black dot between sections C and D. What is the velocity at that exact moment in time? What is the object doing? Is it still accelerating? Why or why not?
3. The motion of a two-stage rocket is portrayed by the following velocity-time graph. Several students analyze the graph and make the following statements. Indicate whether the statements are correct or incorrect. Justify your answers by referring to specific features about the graph. A) After 4 seconds, the rocket is moving in the negative direction (i.e., down). Correct? Yes or No Justification: B) The rocket is traveling with a greater speed during the time interval from 0 to 1 second than the time interval from 1 to 4 seconds. Correct? Yes or No Justification: C) The first engine burns out quickly, but provides a higher acceleration. Correct? Yes or No Justification: D) During the time interval from 4 to 9 seconds, the rocket is moving in the positive direction (up) and slowing down. Correct? Yes or No Justification: E) At nine seconds, the rocket has returned to its initial starting position. Correct? Yes or No Justification: F) During the time interval from 9 to 14 seconds, the rocket is slowing down in the negative direction. Correct? Yes or No Justification:
4. The following graph shows Shopping Sandy s velocity as she races up and down the walkway in North Star Mall trying to find the perfect pair of capris. Answer the questions below. 6 Velocity (m/s) 4 2 0-2 -4-6 0 4 8 12 16 20 24 28 32 36 40 A) Describe Sandy s motion. B) During what time periods is Sandy accelerating? Find Sandy s acceleration for each time period. C) What is Sandy s displacement from t = 6s to t = 14s? D) What is Sandy s displacement from t = 14 s to t = 22 s? E) What is Sandy s displacement from t = 30s to t = 36s?
Unit I-B: Constant Acceleration Worksheet 5 1. A bicycle starts from rest and reaches a speed of 2.5 m/s during a time of 5 seconds. A) Draw a velocity-time graph for the bicycle. 5 Velocity (m/s) B) What was the bicycle s acceleration? C) How far did the bicycle travel during this time? 14 2. A resting cat gets startled by a dog. It turns and runs with an acceleration of 8 m/s 2, reaching full speed in only 0.8 seconds. A) What is its final velocity? 5 Velocity (m/s) B) What distance does the cat cover as it accelerates? C) Make a velocity-time graph for the cat. 14 3. An old clunker car can accelerate from rest to a speed of 28 m/s in 20 s. A) Draw a velocity-time graph for the car. 5 Velocity (m/s) B) What is the average acceleration of the car? C) What distance does it travel in this time? 14
4. A motorcycle goes from 15 m/s to a dead stop in 3 seconds. A) Draw a velocity-time graph for the motorcycle. B) What is its acceleration? 5 Velocity (m/s) C) What distance will it travel? 14 5. An ostrich has an acceleration of -2 m/s 2. If it is initially traveling at a velocity of +7.5 m/s, A) How long will it take to completely stop? 5 Velocity (m/s) B) What distance will it travel? C) Draw a velocity-time graph for the ostrich. 14 6. A Hot Wheels car accelerates down a 5-meter long ramp. If the car takes 2.5 seconds to reach the bottom of the ramp, A) What is its acceleration? Velocity (m/s) 5 B) What is the speed of the car at the bottom of the ramp? C) Draw a velocity-time graph for the car. 14
7. An airplane accelerates down a runway at 3.0 m/s 2 for 33 s until is finally lifts off the ground. A) Determine the distance traveled before takeoff. 5 Velocity (m/s) B) What is the airplane s lift-off velocity? 14 C) Draw a velocity-time graph for the airplane. 8. A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distance of 0.840 m. A) Determine the acceleration of the bullet. 5 Velocity (m/s) B) How long was the bullet traveling inside the barrel of the gun? 14 C) Draw a velocity-time graph for the bullet.
Unit I-B: Constant Acceleration Worksheet 6 1. A bear spies some honey and takes off from rest, accelerating at a rate of 2.0 m/s 2. If the honey is 16 m away, how fast will he be going when he reaches it? 2. At t = 0 s, a car has a speed of 30 m/s. At t = 6 s, its speed is 14 m/s. What is its average acceleration during this time interval? 3. A bus initially moving at 20 m/s slows at a rate of 4 m/s each second. A) How long does it take the bus to stop? B) How far does it travel while braking? 4. A physics student skis down a hill, accelerating at a constant 2.0 m/s 2. If it takes her 15 s to reach the bottom, what is the length of the slope?
5. As a car passes, a dog runs down his driveway to chase it with an initial speed of 5 m/s, and uniformly increases his speed to 10 m/s in 2 s. A) What was his acceleration? B) How long is the driveway (TOTAL displacement)? 6. A mountain goat starts a rockslide and the rocks crash down the slope 100 m. If the rocks reach the bottom in 5 s, what is their acceleration? 7. A car whose initial speed is 30 m/s slows uniformly to 10 m/s in 5 seconds. A) Determine the acceleration of the car. B) Determine the displacement of the car.
Unit I-B: Constant Acceleration Worksheet 7: Wile E. Coyote on the Planet Newtonia (Start of Section 2.3 p.58) Wile E slipped off the edge of a tall building and was photographed at one-second intervals as he underwent free fall. Complete the table below, plot final velocity vs. time, then answer the questions. T (s) 0 y (m) V ave (m/s) V f (m/s) 1 2 3 4 5 1. Write the equation for the graph above. 2. Using your graph, determine the value of the acceleration. 3. Using your graph, determine the displacement during the first 3 s. 4. Using the mathematical model, determine the displacement during the first 3 s.
Wile E. Coyote in Free Fall on Newtonia s Moon Wile E. slips off the edge of a cliff and was photographed at one-second intervals as he underwent free fall. Complete the table below, plot final velocity vs. time, then answer the questions. T (s) 0 y (m) V ave (m/s) V f (m/s) 1 2 3 4 5 6 1. Write the equation for the graph above. 2. Using your graph, determine the value of the acceleration. 3. Using your graph, determine the displacement during the first 3 s. 4. Using the mathematical model, determine the displacement during the first 3 s. 5. How does the gravity on Newtonia s moon compare to that of Newtonia?
Unit I-B: Constant Acceleration Worksheet 8: Free Fall 1. A ball is dropped from the top of the Leaning Tower of Pisa, 70 m above the ground. A) How long does it take to hit the ground? B) What will be its velocity the moment it hits the ground? 2. Now the ball is thrown down from the tower with an initial velocity of 3 m/s. A) Now how long does it take to hit the ground? B) What will be its final velocity now? 3. A ball is thrown straight up into the air with an initial velocity of 15 m/s. A) How high does it go? B) What is the ball s hang-time (how long is it in the air)?
4. A kangaroo jumps to a vertical height of 2.5 m. What was its hang-time? 5. You drop a rock in a well and see it hit the bottom in 2 seconds. How deep is the well? 6. A feather is dropped on the moon from a height of 1.40 meters. The acceleration of gravity on the moon is 1.67 m/s 2. Determine the time for the feather to fall to the surface of the moon. 7. Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. 8. Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. 9. Upton Chuck is riding the Giant Drop at Great America. If Upton free falls for 2.6 seconds, what will be his final velocity and how far will he fall?
Unit I-B: Constant Acceleration Worksheet 9: Stacks of kinematics curves Given the following position vs. time graphs, sketch the corresponding velocity vs. time and acceleration vs. time graphs.
For the following velocity vs. time graphs, draw the corresponding position vs. time and acceleration vs. time graphs.
Unit I-B: Constant Acceleration Review Worksheet 1. A) Give a written description to describe the motion of this object. B) Determine the instantaneous velocity of the object at t = 2 s and explain how you did it. C) Assume the initial velocity was 8 m/s; determine the acceleration of the object. D) Sketch a corresponding velocity-time graph. 2. Use the graph to answer the following questions. A) Describe the motion of the object. B) Determine the acceleration of the object from the graph. C) Calculate the object's displacement from 0 to 6 seconds using either the graph or an equation.
3. A car, initially at rest, accelerates at a constant rate of 4.0 m/s 2 for 6 s. How fast will the car be traveling at t = 6 s? (Show your work!) 4. A tailback initially running at a velocity of 5.0 m/s becomes very tired and slows down at a uniform rate of 0.25 m/s 2. How fast will he be running after going an additional 10 meters? 5. A cliff diver jumps from a cliff and lands in the ocean water after 3.5 seconds. A) What is the height of the cliff? B) What was the velocity of the diver upon entering the water? 6. A ball player catches a ball 4 seconds after throwing it vertically upward. A) With what speed did he throw it? B) How high did it go?
7. Using the graph, compare the following quantities for objects A and B. Is A > B, A < B, or A = B? A) Displacement from 0 to 3 s How do you know? This image cannot currently be displayed. B) Average velocity from 0 to 3 s How do you know? C) Instantaneous velocity at 3 s How do you know? 8. For each of the position vs. time graphs shown, draw the corresponding v vs. t and a vs. t graph