ch. 5 a mathematical model of motion milbank high school
TRANSCRIPT
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Ch. 5 A Mathematical Model of Motion
Milbank High School
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Objectives
• Study average and instantaneous velocity along with acceleration.
• Use graphs and equations to solve problems involving moving objects, including free falling objects.
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Ch. 5.1Graphing Motion in One Dimension• Objectives
– Interpret graphs of position versus time for a moving object to determine the velocity of the object
– Describe in words the information presented in graphs and draw graphs from descriptions of motion
– Write equations that describe the position of an object moving at constant velocity
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Position vs. Time Graphs
It’s obvious!
Plots the position vs the time of an object.
Velocity in this graph is
constant!
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Is it always constant?
No!
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Constant vs. Changing
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Two or more objects
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Ex. Problems
• Pg. 83– Data from a Position-Time Graph
• Pg. 84– Interpreting Position-Time Graphs
• Pg. 85– Describing Motion from a Position-Time
Graph
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Uniform Motion
• Means that equal displacements occur during successive equal time intervals
• Pg 86, Fig 5-6
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Determining the Slope of a Line
• Pick two points on the line and determine their coordinates.
• Determine the difference in y-coordinates of these two points (rise).
• Determine the difference in x-coordinates of these two points (run).
• Divide the difference in y-coordinates (rise) by the difference in x-coordinates (run).
• Slope = rise/run.
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What is the slope?
• Rise = -24 m• Run = 8 seconds• Slope = -3 m/s
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What is the slope?
Rise = 20s
Run = 5m
Slope = 4 m/s
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Using Equations
• While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?
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Or……..
• We can eliminate t0
• Position with constant velocity
d = d0 + vt
t = any value of time
d = position at that time
d0 = position at t = 0
v = velocity
Pg. 88Example Problem
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Practice!
• Pg. 85– Pr. 1-3
• Pg. 87– Pr. 4-8
• Pg. 89– Pr. 9-12
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Sec 5.2
• Graphing Velocity in One Dimension• Basically like 5.1, except velocity isn’t always
constant.• Objectives
– Determine, from a graph of velocity versus time, the velocity of an object at a specified time
– Interpret a v-t graph to find the time at which an object has a specific velocity
– Calculate the displacement of an object from the area under a v-t curve.
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Determining Instantaneous Velocity
• Draw a line tangent to the curve
• The smaller the time interval, the more precise your slope is
• The smaller the time ratio, the closer to the instantaneous velocity you will come
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Velocity-Time Graphs
• It’s obvious!
• Plots the velocity vs. the time
• Gives no information about the position
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Is the velocity constant?
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Displacement from a Velocity-Time Graph
• v = ∆d/∆t
• so….. ∆d = v∆t
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Practice…
• Pg. 93
• Pr. 13-15
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Sec. 5.3
• Acceleration• Determine from the curves on a velocity-
time graph both the constant and instantaneous acceleration
• Determine the sign of acceleration using a v-t graph and a motion diagram
• Calculate the velocity and the displacement of an object undergoing constant acceleration
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Which cars are accelerating??
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Acceleration
• The rate of change of velocity divided by time change
• Usually m/s/s…..or m/s2
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Constant and Instantaneous Acc.
• Constant-straight line on a v-t graph
• Instantaneous-find the slope at a certain point on a v-t graph
• Ex. Pg. 95
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Positive and Negative Acceleration
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Positive and Negative Acceleration
• The sign of the acceleration depends upon the chosen coordinate system
• Fig. 5-13 Pg. 96
• Practice Problems….
• Pg. 97
• Pr. 17-22
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5.4 Free Fall
• Recognize the meaning of acceleration due to gravity
• Define the magnitude of the acceleration due to gravity as a positive quantity and determine the sign of the acceleration relative to the chosen coordinate system
• Use the motion equations to solve problems involving freely falling objects
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Gravity
• Symbol - - “g”
• Acceleration due to gravity= 9.80m/s2
• Be aware of the signs……if upward is your positive direction, then g is going to be negative
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Acceleration due to gravity
• The acceleration of an object in free fall that results from the influence of the Earth’s gravity