Unit 3: One Dimensional Kinematics. Section A: Velocity and Acceleration Corresponding Book...
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Transcript of Unit 3: One Dimensional Kinematics. Section A: Velocity and Acceleration Corresponding Book...
Unit 3:Unit 3:One Dimensional One Dimensional KinematicsKinematics
Section A: Velocity and Section A: Velocity and AccelerationAcceleration
Corresponding Book Sections:Corresponding Book Sections:– 2.2, 2.42.2, 2.4
PA Assessment Anchors:PA Assessment Anchors:– S11.C.3S11.C.3
What is kinematics?What is kinematics?
KinematicsKinematics– The study of motion and how to describe The study of motion and how to describe
itit– Does not consider what causes the Does not consider what causes the
motionmotion
One Dimensional (1D) KinematicsOne Dimensional (1D) Kinematics– Motion in a straight lineMotion in a straight line
Left/right, up/down, east/west, etcLeft/right, up/down, east/west, etc
Coordinate systemCoordinate system
Defines position of an objectDefines position of an object
xf xi x = 0
+
Indicates the positivedirection
Basics of a coordinate Basics of a coordinate systemsystem
Establish a positive directionEstablish a positive direction
Establish an origin (0 point)Establish an origin (0 point)
The origin and positive direction The origin and positive direction must remain the same for the entire must remain the same for the entire problemproblem
Sample ProblemSample Problem
Page 17, Figure 2-2Page 17, Figure 2-2
Set up a coordinate systemSet up a coordinate system– Choose your own originChoose your own origin– Choose the positive directionChoose the positive direction
Distance vs. DisplacementDistance vs. Displacement
DistanceDistance– Total length of travelTotal length of travel– Units: m, cm, mm, kmUnits: m, cm, mm, km
DisplacementDisplacement– Change in position = final - initialChange in position = final - initial x = xx = xff - x - xii
Greek letter “delta”…stands for “Change in”
Back to the sample Back to the sample problem…problem…
Page 17, Figure 2-2Page 17, Figure 2-2
If you leave your friend’s house, go If you leave your friend’s house, go to the supermarket, and come home, to the supermarket, and come home, find the:find the:– DistanceDistance– DisplacementDisplacement
Another example…Another example…
Suppose you leave the grocery store, Suppose you leave the grocery store, stop at your house, go back to the stop at your house, go back to the grocery store, and then go to your grocery store, and then go to your friend’s house. Find the:friend’s house. Find the:– DistanceDistance– DisplacementDisplacement
Last example…Last example…
Suppose you walk from the grocery Suppose you walk from the grocery store to your friend’s house. Find store to your friend’s house. Find the:the:– DistanceDistance– DisplacementDisplacement
What does the negative What does the negative mean?mean?
Remember that we set a certain Remember that we set a certain direction as positive…direction as positive…– Getting a negative simply means that Getting a negative simply means that
we are in the opposite direction as the we are in the opposite direction as the one we established as positiveone we established as positive
– This DOES NOT mean that a negative This DOES NOT mean that a negative number is less than a positive valuenumber is less than a positive value
Before we go any further…Before we go any further…
We need to consistently set up We need to consistently set up problems to make sure we’re problems to make sure we’re following the right steps and make following the right steps and make our work clearour work clear
(And to receive full credit (And to receive full credit ))
Sample Problem SetupSample Problem Setup
Sketch of the Problem
Data Table
ValuesUnknown Variables
Ex:t = 3s
xi = 5 mxf = ?
All Work
Equations UsedStep by-step derivations
(Not division, multiplication, etc)
It takes practice…It takes practice…
It will take practice to start setting up It will take practice to start setting up problems (and not just jumping in to problems (and not just jumping in to solving them)solving them)
In the end, you’ll be more accurateIn the end, you’ll be more accurate
You MUST set up problems like this You MUST set up problems like this on ALL tests, homework assignments, on ALL tests, homework assignments, classwork, etc to receive full credit!classwork, etc to receive full credit!
Speed vs. VelocitySpeed vs. Velocity
SpeedSpeed– Rate of motionRate of motion
– Units: m/s, km/hrUnits: m/s, km/hr
VelocityVelocity– Displacement per Displacement per
unit of timeunit of time
– Units: m/s, km/hrUnits: m/s, km/hr WITH a directionWITH a direction
– N, S, E, W, etcN, S, E, W, etc– + or --+ or --
distanceAverage Speed =
timedisplacement
Average Velocity = time
Sample ProblemSample Problem
You drive 4.0 hr at 30.0 mph and You drive 4.0 hr at 30.0 mph and then another 4.0 hr at 50 mph. Is then another 4.0 hr at 50 mph. Is your average speed:your average speed:– Greater than 40 mphGreater than 40 mph– Equal to 40 mphEqual to 40 mph– Less than 40 mphLess than 40 mph
Find average speed and Find average speed and average velocity for each part average velocity for each part
of the tripof the trip
t = 10 s
t = 50 s
One way to look at One way to look at position vs. time…position vs. time…
Another way…Another way…
Practice problem #1Practice problem #1
Draw a position vs. time graph for Draw a position vs. time graph for the following situation:the following situation:– You walk 2 m from your house in 3 You walk 2 m from your house in 3
secondsseconds– You walk another 3 m in 5 secondsYou walk another 3 m in 5 seconds– You stop for 4 seconds to restYou stop for 4 seconds to rest– You turn around and walk back to your You turn around and walk back to your
house in 6 secondshouse in 6 seconds
Answer…Answer…
Practice problem #2Practice problem #2
Draw a position vs. time graph for Draw a position vs. time graph for the following situation:the following situation:– You walk 10 m toward the school in 5 You walk 10 m toward the school in 5
secondsseconds– You stop to answer your phone for 10 You stop to answer your phone for 10
secondsseconds– You walk back to your car in 5 secondsYou walk back to your car in 5 seconds– You’re late for 1You’re late for 1stst pd, so you walk to the pd, so you walk to the
10 m to school in 3 seconds.10 m to school in 3 seconds.
Answer…Answer…
Instantaneous Speed & Instantaneous Speed & VelocityVelocity
Instantaneous Instantaneous SpeedSpeed– Magnitude of the Magnitude of the
instantaneous instantaneous velocityvelocity
Instantaneous Instantaneous Velocity Velocity – Velocity at one Velocity at one
instant in timeinstant in time
– Unit: m/sUnit: m/s
Speedometer QuestionSpeedometer Question
What does a car’s speedometer What does a car’s speedometer measure?measure?– Average SpeedAverage Speed– Average VelocityAverage Velocity– Instantaneous SpeedInstantaneous Speed– Instantaneous VelocityInstantaneous Velocity
Explain.Explain.
AccelerationAcceleration
The change of velocity with timeThe change of velocity with time
Units: m/sUnits: m/s22, mph/s, etc…, mph/s, etc…
Practice Problem #1Practice Problem #1
Saab advertises a car that goes from Saab advertises a car that goes from 0 to 60 mph in 6.2 seconds. Find the 0 to 60 mph in 6.2 seconds. Find the average acceleration.average acceleration.
Practice Problem #2Practice Problem #2
An airplane has an average An airplane has an average acceleration of 5.6 m/sacceleration of 5.6 m/s22 during during takeoff. How long does it take for takeoff. How long does it take for the plane to reach a speed of 150 the plane to reach a speed of 150 mph?mph?
Acceleration vs. Acceleration vs. DecelerationDeceleration
AccelerationAcceleration– Final speed > Initial Final speed > Initial
SpeedSpeed
DecelerationDeceleration– Final speed < Initial Final speed < Initial
SpeedSpeed
Connection between Connection between acceleration and velocityacceleration and velocity
Situation 1:Situation 1:– Acceleration and Acceleration and
velocity in same velocity in same directiondirection
– Speed of object Speed of object increasesincreases
Situation 2:Situation 2:– Acceleration and Acceleration and
velocity in different velocity in different directionsdirections
– Speed of object Speed of object decreasesdecreases
Practice Problem #1Practice Problem #1
A ferry makes a short run between A ferry makes a short run between two docks. As the ferry approaches two docks. As the ferry approaches the dock (positive x-direction), it has the dock (positive x-direction), it has a speed of 7.4 m/s and slows down to a speed of 7.4 m/s and slows down to a stop in 12.3 s. Find the a stop in 12.3 s. Find the acceleration.acceleration.
Practice Problem #2Practice Problem #2
The ferry now leaves the dock As The ferry now leaves the dock As the ferry approaches the dock, it has the ferry approaches the dock, it has a speed of 7.3 m/s and now slows a speed of 7.3 m/s and now slows down to a stop in 13.1 s. Find the down to a stop in 13.1 s. Find the acceleration.acceleration.
Hint: Think about positive/negative Hint: Think about positive/negative
direction based on last problemdirection based on last problem
The most important The most important acceleration…acceleration…
Recall from other science classes that Recall from other science classes that gravity is always pulling down on gravity is always pulling down on everything.everything.
Gravity has an acceleration Gravity has an acceleration represented by: represented by: gg
gg = 9.81 m/s = 9.81 m/s22 You need to use this exact value
Section B: Kinematics Section B: Kinematics EquationsEquations
Corresponding Book Sections:Corresponding Book Sections:– 2.5, 2.6, 2.72.5, 2.6, 2.7
PA Assessment Anchors:PA Assessment Anchors:– S11.C.3S11.C.3
Motion with Constant Motion with Constant AccelerationAcceleration
Object is either speeding up or Object is either speeding up or slowing downslowing down
Object is just speeding up / slowing Object is just speeding up / slowing down at a constant rate (same down at a constant rate (same acceleration at all times)acceleration at all times)
Velocity as a function of time:
Position as a function of time:
Velocity as a function of position:
Kinematics EquationsKinematics Equations
How do I know when How do I know when to use each equation?to use each equation?
That’s where the sketch and data That’s where the sketch and data table will come in handy…table will come in handy…
Look at what you have, what you’re Look at what you have, what you’re looking for, and find the equation looking for, and find the equation that will include all of those variablesthat will include all of those variables
You may need to use more than one You may need to use more than one equation in a problemequation in a problem
Practice Problem #1Practice Problem #1
A ball is thrown straight upward with A ball is thrown straight upward with an initial velocity of 8.2 m/s. If the an initial velocity of 8.2 m/s. If the acceleration of the ball is that of acceleration of the ball is that of gravity, find the velocity after:gravity, find the velocity after:– 0.50 s0.50 s– 1.0 s1.0 s
Practice Problem #2Practice Problem #2
A boat moves slowly inside a marina A boat moves slowly inside a marina with a constant speed of 1.50 m/s. with a constant speed of 1.50 m/s. As soon as it leaves the marina, it As soon as it leaves the marina, it accelerates at 2.40 m/saccelerates at 2.40 m/s22. Find the:. Find the:– Speed it’s moving after 5.0 sSpeed it’s moving after 5.0 s– Distance it’s traveled after 5.0 s of Distance it’s traveled after 5.0 s of
accelerationacceleration
Practice Problem #3Practice Problem #3
A drag racer starts from rest and A drag racer starts from rest and accelerates at 7.40 m/saccelerates at 7.40 m/s22. How far . How far has it traveled in:has it traveled in:– 1.0 s1.0 s– 2.0 s2.0 s– 3.0 s3.0 s
Review of the Equations…Review of the Equations…
Freely Falling ObjectsFreely Falling Objects
Free Fall -- the motion of an object falling Free Fall -- the motion of an object falling onlyonly under the influence of gravity. under the influence of gravity.
An object is in free fall the moment it is An object is in free fall the moment it is released, whether it’s thrown upward, released, whether it’s thrown upward, downward, or just dropped.downward, or just dropped.
Why don’t we have true free fall on Why don’t we have true free fall on Earth?Earth?
Consider…Consider…
More on gravityMore on gravity Remember…Remember…
– Acceleration due to gravity = Acceleration due to gravity = gg = 9.81 m/s = 9.81 m/s22
That value will be:That value will be:– Positive if our coordinate system has set down as Positive if our coordinate system has set down as
positivepositive
– Negative if our coordinate system has set up as Negative if our coordinate system has set up as positivepositive
Gravity ALWAYS acts in the downward Gravity ALWAYS acts in the downward direction.direction.
+
+
Free Free fall fall
from from restrest
Projectile MotionProjectile Motion