3Kin-e-what?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.One Dimension – dealing only with ________ motion.mechanicsforcesmotionforceslinear
4Familiar 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!DisplacementVelocityAccelerationAlright, let’s share…
5So what do they really mean? SP1. a1Determine the difference between distnace and displacementSP1.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.Answers the question “How far”.Distance is the total amount from the beginning of travelDisplacement is always measured from the origin to the current position.Student walking around demo!!
6So what do they really mean? SP1.a4 Describe the difference between speed and velocity [speed, vavg]Velocity (vavg) is similar to _________ (again, difference later). It is defined as the change in displacement divided by time.Answers the question “How Fast”Speed does not care about directionVelocity changes as direction changesCan you write the equation?speed
7So what do they really mean? SP1.a3 Calculate the velocity of an object. [v=s/t]That equation would beThis is called a definition equation. You will use it to derive other equations in this course.Do you see what the units would be?
8So 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.You must do one of 3 things:Increase velocityDecrease velocityChange directionIf there is no speed change or direction change, there is NO ACCELERATION.Can you write the equation?velocity
9So what do they really mean? 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.
10Looking deeper at Displacement Can you answer the following questions? (avoid using your calculator)A student walks 15 m from the commons, stops at her locker, then continues 20 m to her classroom. What is her displacement?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 m40 m
11Looking Deeper at Displacement SP1.b1 Describe and identiy scalar and vector quantitiesSo 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).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 mscalarvector
12Looking 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.Two other terms to note: ___________ Velocity = v right now _______ Velocity = overall v: (v = (vf + vi)/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.InstantaneousAverage
13Looking Deeper at Velocity Alright, try these two questions on for size: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?A student walks his girlfriend to 1st 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/ss = 0.18 m/s; v=0.083 m/s
14Looking Deeper at Acceleration Constant acceleration - an object will change its velocity by the same amount each second.THIS IS NOT CONSTNAT VELOCITY!!!Non-constant acceleration - an object will change its velocity by different amounts each second.Which one is constant? Non-constant?
15Looking Deeper at Acceleration Since accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value.Time0 - 1 s ~ 5 m/s ~ 5 m ~ 5 m1 -2 s ~ 15 m/s ~ 15 m ~ 20 m2 - 3 s ~ 25 m/s ~ 25 m ~ 45 m3 - 4 s ~ 35 m/s ~ 35 m ~ 80 mLets make 3 quick graphs!Distance traveled in intervalTotal distance traveledVelocity
16Looking Deeper at Acceleration Well, you may be relieved to know that acceleration is a vector qty with no scalar counterpart.So where is the direction?The direction of the acceleration vector depends on two things:whether the object is speeding up or slowing downwhether the object is moving in the + or - direction
17Looking Deeper at Acceleration 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.
18Looking Deeper at Acceleration 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*
19Looking Deeper at Acceleration Which table shows positive acceleration? negative acceleration?A is positive, B is negative.
20Practice…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 looking for?a = 4.0 m/s2
21Practice…A shuttle bus slows down with an average acceleration of –1.8m/s2. 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 looking for?
24Graphing Motion Three types of Graphs: D-T, V-T, A-T What does slope of each represent?This covers all the “concept”, how’s your math skill holding up?
25Position vs Time Graphs Position goes on the vertical axisTime is on the horizontal axis
26Position vs Time Graphs What is the position at time 4s? What about 8s?What is the the avgvelocity? (think back oneslide.)1 m/s
27Position vs Time Graphs Let’s consider this car.The graph would look like this:It would have a constant, rightward (+) velocity
28Position vs Time Graphs Now, let’s consider this other car.It would have a changing rightward (+) velocityThe graph would look like this:
29Position vs Time Graphs 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."Whatever characteristics the velocity has, the slope will exhibit the same (and vice versa).
30Position vs Time Graphs What can you tell me about each objects velocity?Object 1 has a constantpositive velocity.Object 2 has no velocity.Object 3 has a constantnegative velocity.
31Position vs Time Graphs Instantaneous velocity – velocity at a specific point in timeCan be found by the tangent of a curve.
32Position vs Time Graphs What do these graphs tell you about the velocity?Slow, Rightward(+)Constant VelocityFast, Rightward(+)Constant Velocity
33Position vs Time Graphs What do these graphs tell you about the velocity?Slow, Leftward(-)Constant VelocityFast, Leftward(-)Constant Velocity
34Position vs Time Graphs What do these graphs tell you?Negative (-) Velocity, Slow to FastNegative (-) Velocity, Fast to SlowHow would you make this positive?
35PracticeThe following graph represents the motion of a car. What can you tell me about the car’s 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.
36PracticeThe following graph represents the motion of a car. What can you tell me about the car’s 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.
38Four Kinematic Equations Remember:Constant acceleration - an object will change its velocity by the same amount each second.With this idea comes four kinematic equations.Δx = ½(vi + vf) Δtvf = vi + a ΔtΔx = vi Δt + ½ a(Δt)2vf2 = vi2 + 2 a Δx
39Four Kinematic Equations There are always 4 variablesTo use these equations you guess and check.Remember to always do 4 things:Draw a diagramWrite what you knowWrite what you needGuess and checkLet’s practice…
40Four 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/s2. What is the displacement of the car during the skidding process.DiagramKnowns?Unknowns?Equation
41Four 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/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period.DiagramKnowns?Unknowns?Equation
42Four 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.DiagramKnowns?Unknowns?Equation
43Four Kinematic Equations A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8m/s2 for 15s before takeoff. What is its speed at takeoff?DiagramKnowns?Unknowns?Equation
44In a speed boat race the time starts when the boat has a speed of 5m/s 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/s2, with a final velocity of 45m/s. How far was the race?
48Free FallIs when an object is falling under the sole influence of gravityTwo important facts:Free falling objects do not encounter air resistance (in this class)Free fall is a downward acceleration toward earth (the sign gets tricky)
49Free Fall formally known as “acceleration of gravity” = g g = 9.81m/s2 Often times estimated at 10m/s2 or 9.8m/s2There are slight variations that are affected by altitude, we will ignore this.
50Free Fall g is independent of 3 things: time it’s been falling mass of the objectif it started at rest or not
51A deeper look Think of it this way: Δv = 9.8 m/s Δt = 1s This means every 1s the velocity increases 9.8m/s
52A deeper look Think of it this way: So how fast would you be going 3 seconds after jumping out an airplane?How about 5 min?Terminal Velocity – speed when the force of air resistance is equal and opposite to the force of gravity.(around 55m/s for humans)
53A deeper look Time (s) Velocity Δv = 9.8 m/s Δt = 1s 219.6m/s329.4m/s439.2m/s549.0m/sΔv = 9.8 m/sΔt = 1sThis means every 1s the velocity increases 9.8m/s
55Working Backwards It all works backward as well. If a ball is thrown straight up:It will decelerate at 9.81m/s2At the top of it’s path the ball “hangs” in mid air.At bottom of it’s path the balls velocity is equal to viSee Diagram….
56Practice…A worker drops a wrench from the top of a tower 80m tall. What is the velocity when the wrench strikes the ground?DiagramKnowns?Unknowns?Equation
57Practice…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?DiagramKnowns?Unknowns?Equation
58Practice…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?DiagramKnowns?Unknowns?Equation
59Practice makes ….Try thesepg 64 Practice F # 1-4