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Kinematics in One Dimension Chapter 2

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Kin-e-what? Kinematics – the branch of _________ which describes the motion of an object without explicit reference to the ______ that act on the object. Kinematics – the branch of _________ which describes the motion of an object without explicit reference to the ______ that act on the object. Mechanics – the branch of Physics that deals with the ______ of objects and the ______ that change it. Mechanics – the branch of Physics that deals with the ______ of objects and the ______ that change it. One Dimension – dealing only with ________ motion. One Dimension – dealing only with ________ motion. mechanics forces motionforces linear

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Familiar terms? Can you define the following? Take a minute to write down your answer, then, using the same groups for the poster, votefor the best choice. DO NOT look in in your book! Can you define the following? Take a minute to write down your answer, then, using the same groups for the poster, votefor the best choice. DO NOT look in in your book! Displacement Displacement Velocity Velocity Acceleration Acceleration Alright, lets share… Alright, lets share…

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So what do they really mean? SP1. a1Determine the difference between distnace and displacement SP1.a2 Identify the displacement, time and velocity [s, t, v] Displacement (s) is similar to distance. It is, in general, the change in position of an object. Displacement (s) is similar to distance. It is, in general, the change in position of an object. Answers the question How far. Answers the question How far. Distance is the total amount from the beginning of travel Distance is the total amount from the beginning of travel Displacement is always measured from the origin to the current position. Displacement is always measured from the origin to the current position. Student walking around demo!! Student walking around demo!!

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So what do they really mean? SP1.a4 Describe the difference between speed and velocity [speed, v avg ] Velocity (v avg ) is similar to _________ (again, difference later). It is defined as the change in displacement divided by time. Velocity (v avg ) is similar to _________ (again, difference later). It is defined as the change in displacement divided by time. Answers the question How Fast Answers the question How Fast Speed does not care about direction Speed does not care about direction Velocity changes as direction changes Velocity changes as direction changes Can you write the equation? Can you write the equation? speed

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So what do they really mean? SP1.a3 Calculate the velocity of an object. [v=s/t] That equation would be That equation would be This is called a definition equation. You will use it to derive other equations in this course. This is called a definition equation. You will use it to derive other equations in this course. Do you see what the units would be? Do you see what the units would be?

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So what do they really mean? SP1.a6 Calculate the acceleration of an object. Acceleration (a) is the change in ________ of an object divided by the time interval. Acceleration (a) is the change in ________ of an object divided by the time interval. You must do one of 3 things: You must do one of 3 things: Increase velocity Increase velocity Decrease velocity Decrease velocity Change direction Change direction If there is no speed change or direction change, there is NO ACCELERATION. If there is no speed change or direction change, there is NO ACCELERATION. Can you write the equation? Can you write the equation? velocity

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So what do they really mean? Did you get Again, another definition equation. Did you get Again, another definition equation. Special Note: Very rarely does time NOT begin at zero. Therefore, it is very common to write these equations without the Δ symbol by time. Special Note: Very rarely does time NOT begin at zero. Therefore, it is very common to write these equations without the Δ symbol by time.

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Looking deeper at Displacement Can you answer the following questions? (avoid using your calculator) 1. A student walks 15 m from the commons, stops at her locker, then continues 20 m to her classroom. What is her displacement? 2. Another student walks 30 m from the commons before realizing he meant to stop at his locker. He returns 10 m to his locker, then turns back toward his class, 20 m from his locker. What is his displacement? 35 m 40 m

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Looking Deeper at Displacement SP1.b1 Describe and identiy scalar and vector quantities So what makes the difference between 60 m or 40 m for question #2? So what makes the difference between 60 m or 40 m for question #2? The difference is that 60 m is the distance the student travels (a ______ qty), but 40 m is the displacement (a ______ qty). The difference is that 60 m is the distance the student travels (a ______ qty), but 40 m is the displacement (a ______ qty). Vectors take into account the direction of motion. In #2 there was a change of direction. Mathematically, this is a change in sign for the number. So… 30 m + (-10 m) + 20 m Vectors take into account the direction of motion. In #2 there was a change of direction. Mathematically, this is a change in sign for the number. So… 30 m + (-10 m) + 20 m scalar vector

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Looking Deeper at Velocity Okay, explanation first this time. Speed is the scalar qty for velocity. So, speed is magnitude only (just a number). Velocity is magnitude and direction. Okay, explanation first this time. Speed is the scalar qty for velocity. So, speed is magnitude only (just a number). Velocity is magnitude and direction. Two other terms to note: ___________ Velocity = v right now _______ Velocity = overall v: (v = (v f + v i )/2) Two other terms to note: ___________ Velocity = v right now _______ Velocity = overall v: (v = (v f + v i )/2) Remember, a + or – count as direction. You do not have to say north, south, toward, away, etc., but you may see them in a question. Remember, a + or – count as direction. You do not have to say north, south, toward, away, etc., but you may see them in a question. Instantaneous Average

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Looking Deeper at Velocity Alright, try these two questions on for size: 1. A driver traveling north on I-85 notes that it takes 2 minutes to get from exit 99 to exit 101, a distance of 3168 m. What is the drivers speed in m/s? What is her velocity? 2. A student walks his girlfriend to 1 st period, a distance of 40 m from the cafeteria. He turns back toward the cafeteria to his class, 15 m away. This takes 5 minutes. What is his speed? His velocity? Speed = 26.4 m/sVelocity = 26.4 m/s s = 0.18 m/s; v=0.083 m/s

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Looking Deeper at Acceleration Constant acceleration - an object will change its velocity by the same amount each second. Constant acceleration - an object will change its velocity by the same amount each second. THIS IS NOT CONSTNAT VELOCITY!!! THIS IS NOT CONSTNAT VELOCITY!!! Non-constant acceleration - an object will change its velocity by different amounts each second. Non-constant acceleration - an object will change its velocity by different amounts each second. Which one is constant? Non-constant? Which one is constant? Non-constant?

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Looking Deeper at Acceleration Since accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value. Since accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value.Time s~ 5 m/s~ 5 m~ 5 m s~ 5 m/s~ 5 m~ 5 m 1 -2 s~ 15 m/s~ 15 m~ 20 m 1 -2 s~ 15 m/s~ 15 m~ 20 m s~ 25 m/s~ 25 m~ 45 m s~ 25 m/s~ 25 m~ 45 m s~ 35 m/s~ 35 m~ 80 m s~ 35 m/s~ 35 m~ 80 m Lets make 3 quick graphs! Lets make 3 quick graphs! Velocity Distance traveled in interval Total distance traveled

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Looking Deeper at Acceleration Well, you may be relieved to know that acceleration is a vector qty with no scalar counterpart. Well, you may be relieved to know that acceleration is a vector qty with no scalar counterpart. So where is the direction? So where is the direction? The direction of the acceleration vector depends on two things: The direction of the acceleration vector depends on two things: whether the object is speeding up or slowing down whether the object is speeding up or slowing down whether the object is moving in the + or - direction whether the object is moving in the + or - direction

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Looking Deeper at Acceleration A positive acceleration occurs, when an object is speeding up. Acceleration is in the same direction as the velocity. A positive acceleration occurs, when an object is speeding up. Acceleration is in the same direction as the velocity. A negative acceleration occurs, when an object is slowing down. Acceleration is in the opposite direction as the velocity. A negative acceleration occurs, when an object is slowing down. Acceleration is in the opposite direction as the velocity.

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Looking Deeper at Acceleration The general RULE OF THUMB is: The general RULE OF THUMB is: If an object is slowing down, then its acceleration is in the opposite direction of its motion. *See demo*

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Looking Deeper at Acceleration Which table shows positive acceleration? negative acceleration? Which table shows positive acceleration? negative acceleration? A is positive, B is negative. A is positive, B is negative.

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Practice… So… a car traveling at 10 m/s in a straight line speeds up to 30 m/s in 5.0 s. What is the average acceleration? So… a car traveling at 10 m/s in a straight line speeds up to 30 m/s in 5.0 s. What is the average acceleration? What are we given? What are we given? What are we looking for? What are we looking for? a = 4.0 m/s 2

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Practice… A shuttle bus slows down with an average acceleration of –1.8m/s 2. How long does it take the bus to slow from 9.0 m/s to a complete stop? A shuttle bus slows down with an average acceleration of –1.8m/s 2. How long does it take the bus to slow from 9.0 m/s to a complete stop? What are we given? What are we given? What are we looking for? What are we looking for?

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Practice… Practice makes perfect!!! Practice makes perfect!!!

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Represented as graphs Well get to that later…. Well get to that later….

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Graphing Motion Three types of Graphs: D-T, V-T, A-T Three types of Graphs: D-T, V-T, A-T What does slope of each represent? What does slope of each represent? This covers all the concept, hows your math skill holding up? This covers all the concept, hows your math skill holding up?

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Position vs Time Graphs Position goes on the vertical axis Position goes on the vertical axis Time is on the horizontal axis Time is on the horizontal axis

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Position vs Time Graphs What is the position at time 4s? What about 8s? What is the position at time 4s? What about 8s? What is the the avg What is the the avg velocity? (think back one slide.) 1 m/s 1 m/s

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Position vs Time Graphs Lets consider this car. Lets consider this car. The graph would look like this: The graph would look like this: It would have a constant, rightward (+) velocity It would have a constant, rightward (+) velocity

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Position vs Time Graphs Now, lets consider this other car. Now, lets consider this other car. It would have a changing rightward (+) velocity It would have a changing rightward (+) velocity The graph would look like this: The graph would look like this:

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Position vs Time Graphs The shapes of the position versus time graphs reveal reveals useful information about the velocity of the object. The shapes of the position versus time graphs reveal reveals useful information about the velocity of the object. It is often said, "As the slope goes, so goes the velocity." It is often said, "As the slope goes, so goes the velocity." Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa). Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa).

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Position vs Time Graphs What can you tell me about each objects velocity? What can you tell me about each objects velocity? Object 1 has a constant Object 1 has a constant positive velocity. Object 2 has no velocity. Object 2 has no velocity. Object 3 has a constant Object 3 has a constant negative velocity.

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Position vs Time Graphs Instantaneous velocity – velocity at a specific point in time Instantaneous velocity – velocity at a specific point in time Can be found by the tangent of a curve. Can be found by the tangent of a curve.

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Position vs Time Graphs What do these graphs tell you about the velocity? What do these graphs tell you about the velocity? Slow, Rightward(+)Constant Velocity Slow, Rightward(+)Constant Velocity Fast, Rightward(+)Constant Velocity Fast, Rightward(+)Constant Velocity

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Position vs Time Graphs What do these graphs tell you about the velocity? What do these graphs tell you about the velocity? Slow, Leftward(-)Constant Velocity Slow, Leftward(-)Constant Velocity Fast, Leftward(-)Constant Velocity Fast, Leftward(-)Constant Velocity

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Position vs Time Graphs What do these graphs tell you? What do these graphs tell you? Negative (-) Velocity, Slow to Fast Negative (-) Velocity, Slow to Fast Negative (-) Velocity, Fast to Slow Negative (-) Velocity, Fast to Slow How would you make this positive? How would you make this positive?

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Practice The following graph represents the motion of a car. What can you tell me about the cars motion based on the graph? The following graph represents the motion of a car. What can you tell me about the cars motion based on the graph? The car has a rightward velocity. The car has a changing velocity. The car is moving from slow to fast since the slope changes from small big. The car has a rightward velocity. The car has a changing velocity. The car is moving from slow to fast since the slope changes from small big.

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Practice The following graph represents the motion of a car. What can you tell me about the cars motion based on the graph? The following graph represents the motion of a car. What can you tell me about the cars motion based on the graph? The car has a negative velocity. The car has a changing velocity. The car is moving from slow to fast since the slope changes from small to big. The car has a negative velocity. The car has a changing velocity. The car is moving from slow to fast since the slope changes from small to big.

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Four Kinematic Equations

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Remember: Remember: Constant acceleration - an object will change its velocity by the same amount each second. Constant acceleration - an object will change its velocity by the same amount each second. With this idea comes four kinematic equations. With this idea comes four kinematic equations. Δx = ½(v i + v f ) Δt Δx = ½(v i + v f ) Δt v f = v i + a Δt v f = v i + a Δt Δx = v i Δt + ½ a(Δt) 2 Δx = v i Δt + ½ a(Δt) 2 v f 2 = v i a Δx v f 2 = v i a Δx

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Four Kinematic Equations There are always 4 variables There are always 4 variables To use these equations you guess and check. To use these equations you guess and check. Remember to always do 4 things: Remember to always do 4 things: 1. Draw a diagram 2. Write what you know 3. Write what you need 4. Guess and check Lets practice… Lets practice…

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Four Kinematic Equations Ima Hurryin is approaching a stoplight moving with a velocity of m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is m/s 2. What is the displacement of the car during the skidding process. Ima Hurryin is approaching a stoplight moving with a velocity of m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is m/s 2. What is the displacement of the car during the skidding process. Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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Four Kinematic Equations Ben Rushin is is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s 2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Ben Rushin is is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s 2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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Four Kinematic Equations A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its parachute and brakes and comes to rest 3.5s later. What is the distance that it takes the car to stop. A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its parachute and brakes and comes to rest 3.5s later. What is the distance that it takes the car to stop. Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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Four Kinematic Equations A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/s 2 for 15s before takeoff. What is its speed at takeoff? A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/s 2 for 15s before takeoff. What is its speed at takeoff? Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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In a speed boat race the time starts when the boat has a speed of 5m/s. It accelerates at a constant rate of 3.3m/s 2, with a final velocity of 45m/s. How far was the race? In a speed boat race the time starts when the boat has a speed of 5m/s. It accelerates at a constant rate of 3.3m/s 2, with a final velocity of 45m/s. How far was the race?

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Practice makes …. Try these Try these pg 53# 1-2, pg 55# 1-2, pg 58#1-3

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Free Fall!!!! (show video)

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Free Fall!!!!

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Free Fall Is when an object is falling under the sole influence of gravity Is when an object is falling under the sole influence of gravity Two important facts: Two important facts: Free falling objects do not encounter air resistance (in this class) Free falling objects do not encounter air resistance (in this class) Free fall is a downward acceleration toward earth (the sign gets tricky) Free fall is a downward acceleration toward earth (the sign gets tricky)

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Free Fall formally known as acceleration of gravity = g formally known as acceleration of gravity = g g = 9.81m/s 2 g = 9.81m/s 2 Often times estimated at 10m/s 2 or 9.8m/s 2 Often times estimated at 10m/s 2 or 9.8m/s 2 There are slight variations that are affected by altitude, we will ignore this. There are slight variations that are affected by altitude, we will ignore this.

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Free Fall g is independent of 3 things: g is independent of 3 things: time its been falling time its been falling mass of the object mass of the object if it started at rest or not if it started at rest or not

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A deeper look Think of it this way: Think of it this way: Δv = 9.8 m/s Δv = 9.8 m/s Δt = 1s Δt = 1s This means every 1s the velocity increases 9.8m/s This means every 1s the velocity increases 9.8m/s

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A deeper look Think of it this way: Think of it this way: So how fast would you be going 3 seconds after jumping out an airplane? So how fast would you be going 3 seconds after jumping out an airplane? How about 5 min? How about 5 min? Terminal Velocity – speed when the force of air resistance is equal and opposite to the force of gravity. Terminal Velocity – speed when the force of air resistance is equal and opposite to the force of gravity. (around 55m/s for humans) (around 55m/s for humans)

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A deeper look Δv = 9.8 m/s Δv = 9.8 m/s Δt = 1s Δt = 1s This means every 1s the velocity increases 9.8m/s This means every 1s the velocity increases 9.8m/s Time (s)Velocity 19.8m/s 219.6m/s 329.4m/s 439.2m/s 549.0m/s

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Working Backwards It all works backward as well. It all works backward as well. If a ball is thrown straight up: If a ball is thrown straight up: It will decelerate at 9.81m/s 2 It will decelerate at 9.81m/s 2 At the top of its path the ball hangs in mid air. At the top of its path the ball hangs in mid air. At bottom of its path the balls velocity is equal to v i At bottom of its path the balls velocity is equal to v i See Diagram…. See Diagram….

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Practice… A worker drops a wrench from the top of a tower 80m tall. What is the velocity when the wrench strikes the ground? A worker drops a wrench from the top of a tower 80m tall. What is the velocity when the wrench strikes the ground? Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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Practice… Jason hits a volleyball so that it moves with and initial velocity of 6m/s straight upward. If the volleyball start 2m above the floor. How long will it be in the air before it strikes the floor? Jason hits a volleyball so that it moves with and initial velocity of 6m/s straight upward. If the volleyball start 2m above the floor. How long will it be in the air before it strikes the floor? Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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Practice… A ball is thrown straight up into the air at an initial velocity of 25m/s. How long does it take for it to reach the top of its path? How far up does it travel? A ball is thrown straight up into the air at an initial velocity of 25m/s. How long does it take for it to reach the top of its path? How far up does it travel? Diagram Diagram Knowns? Knowns? Unknowns? Unknowns? Equation Equation

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Practice makes …. Try these Try these pg 64 Practice F # 1-4

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Practice makes …. Homework Homework pg 59 # 1-3, 5-6

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