Last class…
Chapter 1. Introduction
Math Review: Powers and exponents
Prefixes for units
Conversion of units
Dimensional analysis
Today…
Chapter 2. Motion in 1-dimension
Position and displacement
Speed and velocity
Motion with a constant velocity
Acceleration
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Chapter 2. Motion in 1-dimension
Why do we study motion?
A lot of things move !
Simplest kind of motions
Æ Motion along a straight line
(i.e., 1-dimensional motion)
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Position
What is motion?
Change of position over time
How to represent position along a straight line:
define: x = 0 some position (Origin)
positive direction for x
length unit, e.g., meter
Position of ball: x = +3 m
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Displacement
Displacement : Change in position
x2 = -2 m
x1 = +3 m
(Displacement) =
∆x =-2m-(+3m)= -5 m
+ or – sign represents direction
Length unit, e.g., meter
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Average velocity, vavg
(Average velocity between time t1 and t2)= vavg
=
x(t2 ) − x(t1 ) x2 − x1
∆x = (Displacement)
=
=
(Time change)
t2 − t1
t2 − t1
∆t
Unit : [Length]/[Time], e.g., m/s
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Average speed, savg
(Average speed between time t1 and t2)= savg
= (Total distance)
(Time change)
Distance does not care about direction, unlike displacement
Distance & savg : always positive, no direction
In general, Distance = Displacement
Average speed = Average velocity
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Example:
Displacement, distance, average velocity, average speed
X=0 km
t = 0 min
x = 50 km
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Example:
Displacement, distance, average velocity, average speed
X=0 km
x = 50 km
t = 50 min
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Example:
Displacement, distance, average velocity, average speed
x = 50 km
t = 50 min
X=0 km
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Example:
Displacement, distance, average velocity, average speed
Between t1=0 and t2=100 min,
find displacement, distance, average velocity, average speed
X=20 km
t = 100 min
x = 50 km
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Math review: Slope of a line
See notes
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Graphical interpretation of average velocity
(Average velocity between time t1 and t2)= vavg
x −x
= 2 1
t2 − t1
=
∆x
∆t
= (Displacement)
(Time change)
ÆSlope of the green line
joining (t1,x1), (t2,x2)
in x vs. t plot
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Instantaneous velocity, or velocity
Instantaneous velocity, or simply, velocity
= Average velocity between
t and t+∆t ,
where ∆t is tiny (or, ∆t → 0 limit)
ÆSlope of tangential
line at t for x vs. t curve
x (m)
Æ How fast at a given time t
t (s)
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Motion with a constant velocity, v
x(t) vs. t :
v = vavg =
x(t ) − x0
Æ x (t ) − x0 = v t Æ
t −0
x = x0 + v t
Instantaneous Speed, or Speed
(Instantaneous Speed) = (magnitude of instantaneous velocity)
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iClicker Quiz
Average velocity between 20 s and 30 s is
(a) positive
(b) zero
(c) negative
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iClicker Quiz
Instantaneous velocity at 30 s is
(a) positive
(b) zero
(c) negative
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iClicker Quiz
Velocity at 10 s is
(a) positive
(b) zero
(c) negative
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Motivation to study acceleration
Velocity changes !
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Average acceleration
(Average acceleration between time t1 and t2) = aavg
=
v(t2 ) − v(t1 ) v2 − v1 ∆v = (Velocity change)
=
=
(Time change)
t2 − t1
t2 − t1 ∆t
Unit: (m/s)/s=m/s2
[aavg]=L/T2
velocity
ÆSlope of the line
joining (t1,v1), (t2,v2)
in v vs. t plot
time
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Instantaneous acceleration
Instantaneous acceleration, or simply, acceleration
= Average acceleration between t and t+∆t ,
where ∆t is tiny (or, ∆t → 0 limit)
ÆSlope of tangential line at t for v vs. t curve
velocity (m/s)
time (s)
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iClicker Quiz: The acceleration between 0 s and 2 s is ______
(a) Positive (b) zero (c) negative (d) Not enough information
v2 = - 20 m/s
t2 = 2 s
Example:
v1 = - 10 m/s
t1 = 0 s
Find average acceleration between 0 s and 2 s.
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Announcement
HW #1: Introduction (Due 1 pm central time, 9/14, Monday).
HW #2: Motion in 1-d (Due 11 pm central time, 9/16, Wednesday).
If you have a difficulty with HW website, contact me.
Paper Quiz on Monday, Sep. 14th.
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