motion in one dimension average versus instantaneous
TRANSCRIPT
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Motion in One Dimension
Average Versus Instantaneous
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Position-Time Graph
Where is the animal at time t = 0?
What time corresponds to a position of zero?
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Slope of a Position-Time Graph
What is the slope of a position-time graph?
Is this graph constant velocity or not?
What would the velocity-time graph look like for the graph on the last slide?
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Distance Versus Displacement
Which one is a vector quantity?
What is the displacement?
What is the distance traveled?
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Average Velocity
Average Speed is total distance divided by total time or the average slope of the line or curve
Instantaneous Speed
txv /
t 0v x tlim /
v dx dt /
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Graphing
•Position-time graph—slope is the speed
•Velocity-time graph—slope is the acceleration
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Slopes
Velocity Acceleration
v dx dt /
a dv dt /
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Problem
A car is located at 30 m at point A, 50 m at point B, 40 m at point C, 0 m at point D, -40 m at point E and –50 m at point F. Equal time intervals separate each point. Sketch the position versus time graph. Find the displacement, average velocity and average speed of the car between A and F.
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Problem 2
A particle moves along the x-axis. Its position varies with time according to the expression x = -4t + 2t2 where x is in meters and t is in seconds. A)Determine the displacement of the particle in the time intervals t = 0 to t = 1 sec and t = 1 sec to t = 3 sec. B) Calculate the average velocity during these two time intervals. C) Find the instantaneous velocity at time t = 2.5 sec.
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Problem 3
The position of an object is given by the equation x(t) = 2 + 4t – t2, where position is measured in meters and time in seconds. What is the particle’s average acceleration from t = 0 to t = 2?
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Homework
Chapter 2 Questions 1,5,7 Problems 2,5,7,11,16,19
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Unique Situation Equations
All of these equations assume constant acceleration:
v v ato
v v a xo
2 2 2
x v t ato 1
22
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Derive These
a dv dt /
dv adt
dv a dt
v at C
dv adtt
v a C
v C
v v ato
o
0
00 ( )
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Derive Some More
dx vdt
dx vdt
dx v at dt
x v t at
o
o
( )
/1 2 2
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Gravity
Acceleration is a constant, g. All these equations apply.
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Homework
Problems 23, 29, 32, 35, 38, 39, 41, 44, 47, 55, 57, 62