UNIT A SUMMARY KEY CONCEPTS CHAPTER SUMMARY 1 Constant velocity represents uniform motion. Distance and Displacement Position-time graphs Average speed and average velocity Positive, negative, and zero average velocity Instantaneous velocity Finding displacement from velocity-time graphs Drawing position-time graphs from velocity-time graphs Position is defined by a reference point and a coordinate system. (1.1) Change in position is a proof for motion; and motion results in change in position. (1.1) Distance is the length of the actual path travelled. It is a scalar quantity. (1.1) Displacement is the length of the straight line between the initial and final positions. It is a vector quantity. (1.1) A position-time graph for an object moving at a constant velocity is a straight line with a non-zero slope. (1.1) Motion with constant velocity is called uniform motion. (1.2) The slope of a straight line position-time graph gives the velocity. The slope of the tangent at a point on a curved position-time graph gives instantaneous velocity. (1.2) Average speed is distance covered per unit time and average velocity is displacement per unit time. (1.2) The sign of velocity gives the direction of motion. (1.2) The area under a velocity-time graph represents displacement; the slope represents acceleration. (1.2) 2 Acceleration causes a change in velocity. Non-uniform motion Uniform or constant acceleration Speeding up and Slowing down Slope of a velocity-time graph Acceleration Acceleration-time graph from velocity-time graph Equations of motion for uniform acceleration (Kinematics equations) Change in velocity is evidence of acceleration. (2.1) Acceleration is defined as the rate of change in velocity. (2.1) Acceleration is a vector quantity. (2.1) The same signs for velocity and acceleration mean speeding up. (2.1) Opposite signs for velocity and acceleration mean slowing down. (2.1) The position-time graph for an object undergoing uniformly accelerated motion is a curve. The corresponding velocity-time graph is a straight line with non-zero slope. The corresponding acceleration-time graph is a horizontal line. (2.2) You can draw acceleration-time and position-time graphs by calculating and plotting the slope and area, respectively, of a velocity-time graph. (2.2) There are five kinematics equations for constant acceleration: v f v i a t, d ( v v f i 2 ) t, d v i t 1_ 2 a ( t) 2, d v f t 1_ 2 a ( t) 2 2 2, and v f v i 2 a d. (2.3) When solving problems in kinematics, choose the equation that contains three known variables, so you solve for the unknown value. (2.3) 3 A projectile is an object moving in a vertical plane, under the influence of the force of gravity. Gravity causes objects to accelerate downward Projectile motion straight down is free fall Maximum height Components of vectors Projectile motion in two dimensions An object falling only under the influence of gravity undergoes free fall. (3.1) Objects fall with a constant vertical acceleration equal to g (down). (3.1) The acceleration and velocity of an object in free fall depend only the height. (3.1) The acceleration and velocity of an object do not depend on the mass of the object. (3.1) Gravity causes objects to accelerate downward. (3.2) Projectiles are objects undergoing two-dimensional motion under the influence of gravity. (3.2) Two dimensional vectors can be resolved into x and y components. (3.2) Horizontal and vertical components of projectile motion are independent. (3.2) The shape of a projectile s trajectory is a parabola. (3.3) At maximum height, a projectile s vertical velocity is zero. (3.3) The time taken to reach maximum height equals the time taken to fall back down to the original height. (3.3) 88 Unit A Summary
UNIT A REVIEW ACHIEVEMENT CHART CATEGORIES k Knowledge and understanding t Thinking and investigation c Communication a Application Key Terms Review 1. Using your own words, define these terms. c acceleration acceleration due to gravity displacement distance instantaneous velocity kinematics magnitude non-uniform motion origin position projectile projectile motion range scalar quantity tangent trajectory uniform motion uniformly accelerated motion vector quantity velocity Key Concept Review CHAPTER 1 2. What is the condition in which distance and displacement have the same magnitude? Give an example when they are not the same. k 3. Is it possible to have non-zero average speed, but zero average velocity for an object s motion? Explain. k 4. Sketch two different position-time graphs for objects with a negative velocity. c CHAPTER 2 5. Sketch a position-time graph for each statement below. Assume that right is positive. (a) object accelerating to the right t (b) object accelerating to the left t (c) object travelling at a constant velocity left t (d) object at rest t (e) object travelling at a constant velocity right t 6. If an object is slowing down, it means that its acceleration is negative. Is this true? Explain. c 7. Sketch two different velocity-time graphs for objects with a negative acceleration. c 8. Solve each of the following equations for initial velocity algebraically. (a) a v f v i k t (b) d v i t 1_ a ( t)2 k 2 (c) d 1_ 2 ( v i v f ) t k CHAPTER 3 9. Resolve the following vectors into their components. (a) 5.0 m [90 ] k (b) 16.0 m/s [20 S of W] k 10. Using an appropriate scale and reference coordinates, draw the following vectors. (a) 5.0 m/s [0 ] k (b) 25.0 m/s 2 [60 N of E] k (c) 1.50 km [120 ] k 11. Using a scale of 1.0 cm : 3.5 km, determine the magnitude N and direction of the vector below. k W Question 11 Connect Your Understanding 12. A wildlife biologist records a moose s position as it swims away from her. Using the graph below, determine the moose s velocity. a Position (m [W]) 3 25.0 15.0 5.0 0 0 2.0 4.0 6.0 8.0 Question 12 S Position vs. Time 12.0 R E Unit A Review 89
13. Hockey pucks can be shot at speeds of 107 km/h. If a puck is shot at an angle of 30, determine how long the puck is in the air, how far it will travel, and how high it will be at the peak of its trajectory. a 14. From the position-time graph below, determine which object has the greatest velocity. k Position (m [forward]) Question 14 15. The longest kickoff in CFL history was 83.2 m. If the ball remained in the air for 4.12 s, determine its initial speed. a 16. Determine the speed of a raven that travels 48 km in 90 min. a 17. Describe the motion of the object illustrated in the graph below. c Velocity (m/s [E]) A Velocity vs. Time 9.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0 0 2.0 4.0 6.0 8.0 Question 17 18. A circular track has a radius of 70 m. The starting point is taken as the origin. (a) What is a runner s displacement when he has completed half a lap? a (b) How much distance has he covered when he completes half a lap? Is it the same as the displacement? Explain? c (c) Compare the distance covered and the displacement of the runner when he has completed a full lap. k 90 Unit A Review D C B 12.0 19. Two skateboarders approach each other on a straight road. Their respective constant speeds are 5.5 m/s and 6.5 m/s. If they are initially 200 m apart, when and where do they meet? a 20. A car s speed increases from 16.0 m/s to 27.0 m/s in 5.0 s. (a) What is the acceleration of the car? a (b) What is the distance covered by the car during this time? a 21. A train is moving on a straight track with a speed of 7 km/h. It slows down within a distance of 35.0 m. During this time, the train s acceleration was 2.0 m/s 2. (a) What is the final speed of the train? a (b) How much time did the train take to slow down to this speed? a 22. A student pushes a block across a 60-cm high table. The block slides over the edge of the table with a horizontal velocity of 1.5 m/s and hits the ground. (a) For how long is the block in the air? a (b) How far from the table does the block fall on the ground? a (c) What are the x and y components of the velocity just before the block hits the ground? k 23. (a) What is the change in velocity in s, as illustrated in the acceleration-time graph below? k (b) If the object had an initial velocity of 10 m/s [forward], what is its final velocity after s? k Acceleration (m/s 2 [forward]) 4.0 3.0 2.0 1.0 2.0 4.0 6.0 8.0 Question 23 Acceleration vs. Time 24. How far will a crow fly at 13.4 m/s for 15.0 min? a 25. How long will it take a car to travel 650 km if its speed is 100 km/h? a 26. A baseball player hits a baseball with a velocity of 30 m/s [25 ]. If an outfielder is 85.0 m from the ball when it is hit, how fast will she have to run to catch the ball before it hits the ground? a
27. Determine the magnitude of the acceleration of a Jeep Grand Cherokee if its stopping distance is 51.51 m when travelling at 113 km/h. a 28. An object undergoing uniformly accelerated motion has an initial speed of 11.0 m/s and travels 350 m in 3.00 s. Determine the magnitude of its acceleration. k 29. Improperly installed air conditioners can occasionally fall from apartment windows down onto the road below. How long does a pedestrian have to get out of the way of an air conditioner falling eight stories (24 m)? k 30. An object is launched from the top of a building with an initial velocity of 15 m/s [32 ]. If the building is 65.0 m high, how far from the base of the building will the object land? k 31. Two friends walk at the same speed of 4.0 km/h. One friend steps onto a travelator (shown below) moving at 3.0 km/h. If he maintains the same initial walking speed, (a) how long will it take him to reach the end of the 100-m-long travelator? k (b) what must be the magnitude of the acceleration of the other friend to arrive at the end of the travelator at the same time? k 35. What distance will a vehicle travel if it accelerates uniformly from 15.0 m/s [S] to 35.0 m/s [S] in 6.0 s? a 36. From the graph below, determine the instantaneous velocity of the object at 5.0 s, s, and 15.0 s. k Position (m [210 ]) 7 6 5 4 3 5.0 15.0 Question 36 Position vs. Time 37. An object starts from rest and travels 5 m along a frictionless, level surface in 2.75 s. What is the magnitude of its acceleration? k 38. Determine the displacement of a bird from the velocity-time graph below. a 32.0 Velocity vs. Time for a Bird 28.0 Question 31 32. How far will a vehicle travel if it accelerates uniformly at 2.00 m/s 2 [forward] from 2.50 m/s to 7.75 m/s? a 33. An object is thrown into the air with a speed of 25.0 m/s at an angle of 42. Determine how far it will travel horizontally before hitting the ground. k 34. Determine the average velocity of a truck that travels west from Kingston towards Toronto at 110 km/h for 1.0 h and 20 min and then 90 km/h for 100 min. a Velocity (km/h [N]) 24.0 16.0 12.0 8.0 4.0 3 4 Question 38 5 6 39. Sketch a position-time graph for an object that travels at a constant velocity of 5.0 m/s for 10 s, stops for 10 s, then travels with a velocity of 2.0 m/s for 20 s. k 40. Determine the height reached by a projectile if it is released with a velocity of 18.0 m/s [20 ]. k Unit A Review 91
41. The bishop is a chess piece that moves diagonally along one colour of square. Refer to the diagram below. Assuming the first move is toward the left of the board, determine (a) the minimum number of squares the bishop covers in getting to the top right square t (b) the bishop s displacement from the start if the side length of each square is taken as 1 unit and each move is from the centre of a square to the centre of another square t End Position (m [E]) 10 9 8 7 6 5 4 3 Position vs. Time i ii iii iv 2.0 4.0 6.0 Question 45 8.0 Question 41 Start 42. A wildlife biologist notes that she is 350 m [N] from the park ranger station at 8:15 a.m. when she spots a grizzly bear. At 8:30 a.m., she is 1.75 km [N] of the ranger station. Determine the biologist s average velocity. a 43. A bus travels 500 m [N], 200 m [E], and then 750 m [S]. Determine its displacement from its initial position. k 44. Determine the magnitude of the acceleration of a Jeep Grand Cherokee that can reach 26.9 m/s from rest in 4.50 s. a 45. Match the motion with the correct line on the given position-time graph. Identify the motion as at rest, uniform motion, or uniformly accelerated motion. (a) an airplane taking off k (b) an airplane landing k (c) passing a car on the highway k (d) waiting at the red line at Canada Customs k (e) standing watching a parade k (f) travelling along the highway on cruise control k Skills Practice 46. Draw a Venn diagram to illustrate the concepts of graphical analysis. c 47. For an experiment to measure the velocity of an object, you have a radar gun, probeware, and motion sensors. Explain to a classmate how you would decide which instrument to use. c 48. Design an experiment to determine the acceleration of an object rolling down an inclined plane. t 49. Construct a concept map for solving a two dimensional motion problem involving a projectile thrown at an angle. c 50. Explain how you can use velocity-time graphs to describe the motion of an object. c Revisit the Big Ideas and Fundamental Concepts 51. (a) Describe the ways in which cars are designed to minimize consumption at high speeds. c (b) Describe how our understanding of concepts of kinematics benefits society. c 52. Explore and prepare a presentation on how the kinematics principles are used to make graphics for action scenes in a movie? t 92 Unit A Review
53. Investigation of traffic accidents involves extensive use of kinematics principles and equations. Make a flow chart to explain this process. For each part of the flow chart, name the concept and/or the equation that is related to it. c 54. As a future voter, what legislation would you support to improve vehicular and road safety? c 55. Assess how well you are able to graph the motion of an object. Explain how you determine a reference point. c Science, Technology, Society, and the Environment The use of the global positioning system (GPS) increases accuracy in mapping, surveying, navigation, monitoring earthquakes, and tracking the movement of oil spills and forest fires, among other benefits. However, its extensive use raises concerns about privacy and human rights. GPS systems use satellites and the information received is used for various purposes. 56. How are satellites used to track animal species in remote areas? t 57. How can scientists and environmentalists use this information to help protect vulnerable species? t 58. What is the impact of the use of speed limiters and tracking devices in the trucking industry? t 59. What effect do lower truck speeds have on highway safety and vehicle emissions? t Reflection 60. Describe to a classmate which kinematics concepts and laws you found most interesting when studying this unit. Give reasons for your choices. c 61. Identify one issue pertaining to motion studied in this unit that you would like to investigate in greater detail. c 62. What concept in this unit did you find most difficult? What steps could you take to improve your understanding? c A15 Unit Task PHYSICS SOURCE Are Amber Traffic Lights Timed Correctly? Purpose To calculate the stopping distances and go distances at traffic intersections (Figure 3.48) and study the effectiveness of red light cameras to recommend the timings of the amber light Activity Overview In this activity, you will use a measuring tape and a stopwatch. You will measure the length of 10 different intersections near your school. For each of these intersections, you will also record the amber light times. Then, for each intersection calculate the stopping distance and go distance for the posted speed limit and give your recommendations. Your teacher will give you a copy of the full Task. Figure 3.48 Traffic lights at a busy intersection Unit A Review 93