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+Unit 3:One Dimensional Kinematics
+Section A: Velocity and Acceleration
Corresponding Book Sections:2.2, 2.4
PA Assessment Anchors:S11.C.3
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+What is kinematics?
KinematicsThe study of motion and how to describe it
Does not consider what causes the motion
One Dimensional (1D) KinematicsMotion in a straight line
Left/right, up/down, east/west, etc
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+Coordinate system
Defines position of an object
xf xi x = 0
+
Indicates the positivedirection
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+Basics of a coordinate system
Establish a positive direction
Establish an origin (0 point)
The origin and positive direction must remain the same for the entire problem
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+Sample Problem
Page 17, Figure 2-2
Set up a coordinate systemChoose your own originChoose the positive direction
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+Distance vs. Displacement
DistanceTotal length of travelUnits: m, cm, mm, km
DisplacementChange in position = final - initial x = xf - xi
Greek letter “delta”…stands for “Change in”
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+Back to the sample problem…
Page 17, Figure 2-2
If you leave your friend’s house, go to the supermarket, and come home, find the:DistanceDisplacement
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+Another example…
Suppose you leave the grocery store, stop at your house, go back to the grocery store, and then go to your friend’s house. Find the:DistanceDisplacement
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+Last example…
Suppose you walk from the grocery store to your friend’s house. Find the:DistanceDisplacement
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+What does the negative mean?
Remember that we set a certain direction as positive…Getting a negative simply means that we are in the opposite direction as the one we established as positive
This DOES NOT mean that a negative number is less than a positive value
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+Before we go any further…
We need to consistently set up problems to make sure we’re following the right steps and make our work clear
(And to receive full credit )
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+Sample 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)
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+It takes practice…
It will take practice to start setting up problems (and not just jumping in to solving them)
In the end, you’ll be more accurate
You MUST set up problems like this on ALL tests, homework assignments, classwork, etc to receive full credit!
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+Speed vs. Velocity
SpeedRate of motion
Units: m/s, km/hr
Velocity Displacement per unit of time
Units: m/s, km/hrWITH a direction
N, S, E, W, etc+ or --
distanceAverage Speed =
time displacementAverage Velocity =
time
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+Sample Problem
You drive 4.0 hr at 30.0 mph and then another 4.0 hr at 50 mph. Is your average speed:Greater than 40 mphEqual to 40 mphLess than 40 mph
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+Find average speed for each part and average velocity for trip
t = 10 s
t = 50 s
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+Position vs. Time Graph18
+Practice problem #1
Draw a position vs. time graph for the following situation:You walk 2 m from your house in 3 seconds
You walk another 3 m in 5 secondsYou stop for 4 seconds to restYou turn around and walk back to your house in 6 seconds
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+Answer…
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+Practice problem #2
Draw a position vs. time graph for the following situation:You walk 10 m toward the school in 5 seconds
You stop to answer your phone for 10 seconds
You walk back to your car in 5 seconds
You’re late for 1st pd, so you walk to the 10 m to school in 3 seconds.
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+Answer…
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+Instantaneous Speed & Velocity
Instantaneous SpeedMagnitude of the instantaneous velocity
Instantaneous Velocity Velocity at one instant in time
Unit: m/s
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+Speedometer Question
What does a car’s speedometer measure?Average SpeedAverage VelocityInstantaneous SpeedInstantaneous Velocity
Explain.
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+Acceleration
The change of velocity with time
Units: m/s2, mph/s, etc…
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+Practice Problem #1
Saab advertises a car that goes from 0 to 60 mph in 6.2 seconds. Find the average acceleration.
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+Practice Problem #2
An airplane has an average acceleration of 5.6 m/s2 during takeoff. How long does it take for the plane to reach a speed of 150 mph?
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+Acceleration vs. Deceleration
AccelerationFinal speed > Initial Speed
DecelerationFinal speed < Initial Speed
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Connection between acceleration and velocity Situation 1:
Acceleration and velocity in same direction
Speed of object increases
Situation 2: Acceleration and velocity in different directions
Speed of object decreases
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+Practice Problem #1
A ferry makes a short run between two docks. As the ferry approaches the dock (positive x-direction), it has a speed of 7.4 m/s and slows down to a stop in 12.3 s. Find the acceleration.
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+Practice Problem #2
The ferry now leaves the dock As the ferry approaches the dock, it has a speed of 7.3 m/s and now slows down to a stop in 13.1 s. Find the acceleration.
Hint: Think about positive/negative
direction based on last problem
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+The most important acceleration…Recall from other science classes that gravity is always pulling down on everything.
Gravity has an acceleration represented by: g
g = 9.8 m/s2
You need to use this exact value
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+Section B: Kinematics Equations
Corresponding Book Sections:2.5, 2.6, 2.7
PA Assessment Anchors:S11.C.3
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+Motion with Constant AccelerationObject is either speeding up or slowing down
Object is just speeding up / slowing down at a constant rate (same acceleration at all times)
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+
Velocity as a function of time:
Position as a function of time:
Velocity as a function of position:
Kinematics Equations35
+How do I know when to use each equation?That’s where the sketch and data table will come in handy…
Look at what you have, what you’re looking for, and find the equation that will include all of those variables
You may need to use more than one equation in a problem
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+Practice Problem #1
A ball is thrown straight upward with an initial velocity of 8.2 m/s. If the acceleration of the ball is that of gravity, find the velocity after:0.50 s1.0 s
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+Practice Problem #2
A boat moves slowly inside a marina with a constant speed of 1.50 m/s. As soon as it leaves the marina, it accelerates at 2.40 m/s2. Find the:Speed it’s moving after 5.0 sDistance it’s traveled after 5.0 s of acceleration
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+Practice Problem #3
A drag racer starts from rest and accelerates at 7.40 m/s2. How far has it traveled in:1.0 s2.0 s3.0 s
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+Review of the Equations…
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+Freely Falling Objects
Free Fall -- the motion of an object falling only under the influence of gravity.
An object is in free fall the moment it is released, whether it’s thrown upward, downward, or just dropped.
Why don’t we have true free fall on Earth?
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+Consider…
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+More on gravity
Remember… Acceleration due to gravity = g = 9.81 m/s2
That value will be: Positive if our coordinate system has set down as positive
Negative if our coordinate system has set up as positive
Gravity ALWAYS acts in the downward direction.
+
+
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+Free fall from rest
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+Projectile Motion
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