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LECTURE 3
1D MOTION
Instructor: Kazumi Tolich
Lecture 3
2
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Reading chapter 2-1 to 2-6
¤  One
dimensional motion
n  Position,
displacement, and distance
n  Velocity and speed
n  Acceleration
n  Motion with a constant acceleration
Vector and scalar quantities
3
¨ 
A vector quantity has a magnitude and direction.
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¤ 
¤ 
¤ 
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Displacement (m): how far something moved in what direction
Velocity (m/s): how fast something is moving in what direction
Acceleration (m/s2): how fast velocity is changing in what direction
etc.
A scalar quantity has only magnitude.
¤ 
¤ 
¤ 
¤ 
Time (s): how long it has been.
Temperature (K): how hot something is.
Mass (kg): how much stuff there is.
etc.
Coordinate system and position
4
A coordinate system defines the position of an object.
¨  You need to define where the origin is, and which
direction is the positive direction.
¨ 
x0
Initial (x0) and final (xf)
Positions of person
Displacement and distance
5
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¨ 
¨ 
¨ 
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Displacement is the difference in the initial and final positions:
Δx = xf – x0 (in the x direction).
In calculating the displacement of an object, how it traveled
from the initial to the final position does not matter.
Displacement is a vector quantity.
Total distance traveled is total length of travel.
Distance is a scalar quantity.
Clicker question: 1
6
Clicker question: 2
7
Elapsed time
8
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¨ 
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Time is change, or the interval over which change occurs.
The SI unit for time is the second, s.
Elapsed time Δt is
Δt = tf − t0
where tf is the final time, and t0 is the initial time.
¨ 
If we define t0 = 0,
Δt = tf ≡ t
Average velocity and average speed
9
¨ 
The average velocity (in the x direction) is defined to be
v≡
¨ 
Δx xf − x0
=
Δt tf − t0
The average speed of the trip is defined to be
average speed ≡
¨ 
total distance
Δt
Average velocity is a vector quantity, and average speed is
a scalar quantity.
Clicker question: 3
10
Instantaneous velocity and speed
11
¨ 
Instantaneous velocity in the x direction is defined to be
Δx
v ≡ lim
Δt →0 Δt
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Instantaneous velocity is a vector quantity.
Instantaneous speed is the magnitude of the instantaneous
velocity.
Instantaneous vs. average speed
12
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Why is instantaneous speed more interesting to the
highway patrol than average speed?
¤  Suppose
you drive 100 km in one hour. Your average
speed would be 100 km/h.
¤  This is your average speed over the whole trip.
¤  But how likely is it that you were traveling at exactly
100 km/h the whole time?
Average and instantaneous accelerations
13
¨ 
Acceleration is the rate of change of velocity, or how quickly velocity is changing.
Average acceleration in the x direction is defined to be
¨ 
Δv vf − v0
=
Δt tf − t0
Instantaneous acceleration is defined to be
¨ 
a≡
Δv
Δt →0 Δt
a ( t ) ≡ lim
¨ 
¨ 
Acceleration is a vector quantity. It points in the direction of Δv.
When acceleration is constant, the instantaneous and average acceleration are the
same.
Directions of a and v
14
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¨ 
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When the direction of velocity and acceleration are the same, the object is
speeding up.
When the direction of velocity and acceleration are opposite, the object is
slowing down.
When an object slows down, its acceleration is opposite to the direction of
its motion. This is known as deceleration.
Acceleration and force
15
Acceleration is caused by force.
¨  The direction of acceleration of an object is the
same as the force applied to accelerate it.
¨ 
Clicker question: 4
16
Motion with constant acceleration
17
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For an object with an initial position, x0, initial velocity, v0, and
a constant acceleration, a,
¤ 
the velocity, v, as a function of time, t, is given by
v = v0 + at
¤ 
the position, x, as a function of time, is given by
x = x0 + v0t + 12 at 2
¤ 
The velocity as a function of displacement, Δx, is given by
v 2 = v02 + 2a ( x − x0 ) = v02 + 2aΔx
Demo: 1
18
¨ 
Incline with Flash Lights
¤  Demonstration
of the distance and the velocity formula
under a constant acceleration.
1 2
x ( t ) = x0 + v 0 t + at
2
v ( t ) = v0 + at
Example: 1
19
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A motor cycle is moving at
v0 = 30.0m/s when the rider
applies the brakes, giving the
motorcycle a constant
deceleration. At t1 = 3.0s, after
braking begins, the speed
decreases to v1 = 15.0m/s. What
distance does the motorcycle
travel from the instant braking
begins until it comes to rest?
Example: 2
20
¨ 
At t = 0 a ball, initially at
rest, starts to roll down a
ramp with constant
acceleration. Suppose it
moves 1 foot between
t = 0 s and t = 1 sec. How
far does it move between
t = 1sec and t = 2 sec?
?
4ft
9ft
16ft
1ft