Announcement I
Physics 1408-002
Lecture note is on the web
Handout (4 slides/page)
Principles of Physics
Lecture 2
– Chapter 2 –
January 13, 2009
http://highenergy.phys.ttu.edu/~slee/1408/
1408 Lab News: on-going now!!
*** Class attendance is strongly encouraged and will be
taken randomly. Also it will be used for extra credits.
HW Assignment #1 will be placed on
MateringPHYSICS “today”,
and is due by 11:59pm
on Tuesday, 1/20
Sung-Won Lee
Sungwon.Lee@ttu.edu
Announcement II
SI session by
Reginald Tuvilla
SI sessions will be at the following times
and location starting this Thursday.
Monday 4:30 - 6:00pm - Holden Hall 106
Thursday 4:00 - 5:30pm - Holden Hall 106
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Chapter 2
Equations of Constant Acceleration
Describing Motion:
Kinematics in
“One” Dimension
1.!
2.!
3.!
4.!
5.!
6.!
7.!
Reference Frames & Displacement
Average Velocity
Instantaneous Velocity
Acceleration
Motion at Constant Acceleration
Solving Problems
Freely Falling Objects
The directions of the car’s velocity
and acceleration are shown by the
green (v) and gold (a) arrows.
Motion is described using the
concepts of velocity and
acceleration.
We examine in detail motion with
constant acceleration, including the
vertical motion of objects falling
under gravity.
Equations we need to solve constant-acceleration problems
Kinematics-Description of Motion
•!Reference Frames and Displacement
•!Average Velocity
•!Instantaneous Velocity
•!Acceleration
Kinematics
•! Describes motion while ignoring
the agents that caused the motion
•! For now, will consider motion in
one dimension
–! Along a straight line
Position
•! Defined in terms of a frame of reference
–! One dimensional, so generally the x- or y-axis
•! The object’s position is its location with respect to
the reference frame (see next slide)
•!Motion at Constant Acceleration
•!Solving Problems
•!Falling Objects
•!Graphical Analysis of Linear Motion
Reference Frames and Displacement
Any measurement of position, distance, or speed must be made
with respect to a reference frame
e.g. If you are sitting on a train and someone walks down the
aisle, their speed with respect to the train is a few miles
per hour, at most.
Their speed with respect to the ground is much higher.
A person walks toward the front of a train at 5 km/h. The train is moving 80 km/h
with respect to the ground, so the walking person’s speed, relative to the ground,
is 85 km/h.
Reference Frames and Displacement
Distinction between distance and displacement.
Displacement (blue line) is how far the object is from
its starting point, regardless of how it got there.
Distance traveled (dashed line) is measured along the
actual path.
A person walks 70m east, then 30m
west. The total distance traveled is
100 m (path is shown dashed in
black); but the displacement,
shown as a solid blue arrow, is
40m to the east.
Reference Frames and Displacement
•! Defined as the change in position during some time interval
–! Represented as !x; !x = xf – xi (f = final, i = initial)
–! SI unit = meters (m)
–! !x can be positive or negative
The displacement is written:
Left:
Right:
Displacement
is positive
Displacement
is negative
Average Velocity
Speed: how far an object travels in a given time interval
•! Velocity v is the “rate of change of position”
•! Average velocity vav (or v) in the time !t = t2 - t1 is:
Velocity includes directional information:
trajectory
Vav = slope of line connecting x1 and x2
x2
!x
x1
t1
The arrow represents the displacement x2 – x1
!t
t2
Uniform Motion
•! The simplest form of motion is uniform motion. An object’s
motion is uniform if its position-versus-time graph (x,t) is
a straight-line. (see Fig)
t
x(t 2 ) " x(t1 ) #x
vav !
=
t 2 " t1
#t
Example
•! You start in Chicago at 9 am and drive straight west down Iowa,
stopping for tolls, arriving in Aurora 100 km west at 10 am.
What is your average velocity?
•! Let x be the displacement west. Let t1=0 be 9 a.m. and let t2= 1 hour
be the arrival time.
•! Let x(t1 )= x1=0 km be Chicago, and x(t2 )=x2= 100 km be Aurora.
•! The displacement, x2- x1= 100 km
Fig shows how uniform and non-uniform motion appear in (x,t)
graphs. For uniform motion the (average) velocity remains
constant:
•! The time interval,
t2- t1= 1 hour = 3600 s
•! The average velocity, x2- x1 /t2- t1 = 100 km/hr
Instantaneous Velocity
Instantaneous Velocity
The instantaneous velocity is the average velocity, in the limit as
the time interval becomes infinitesimally short.
These graphs show
(a) constant velocity,
(b) varying velocity.
Ideally, a speedometer would measure
instantaneous velocity; in fact, it
measures average velocity, but over a
very short time interval.
What was my velocity
at the instant t = 1s?
Finding Position from Velocity
Reminder!!
2.4 Acceleration
Position, time, and velocity are important concepts, and they
might appear to be sufficient. But that is not the case.
Sometimes an object’s velocity changes as it moves.
Acceleration deals with change of velocity.
i.e. Acceleration is the rate of change of velocity.
Velocity changes if:
the magnitude of the velocity (speed) changes
the direction of the velocity changes
Average acceleration =
Change of velocity
Time interval
Note the same pattern:
"
aavg =
"
!v
!t
"
vavg =
!r"
!t
Three vector quantities:
!
r
v
!
a
!
displacement
velocity
acceleration
meters
meters/second
meters/(second)2
2.4 Acceleration
2-4 Acceleration
Acceleration is a vector, although in one-dimensional motion
we only need the sign (e.g. + or -)
There’s a difference between negative acceleration and deceleration:
Left-hand Fig:: positive acceleration (“increase”)
Right-hand Fig:: negative acceleration (“decrease”)
Negative acceleration is acceleration in the negative direction as
defined by the coordinate system.
Deceleration occurs when the acceleration is opposite in direction to
the velocity.
2-4 Acceleration
Motion at Constant Acceleration
The instantaneous acceleration is the average acceleration,
in the limit as the time interval becomes infinitesimally short.
The average velocity of an object during a time interval t
The acceleration, assumed constant, is
Reminder:: the instantaneous velocity
In addition, as the velocity is increasing at a constant rate, we
know that
Motion at Constant Acceleration
Combining these last three equations, we find:
Motion at Constant Acceleration
We can also combine these equations so as to eliminate t:
We now have all the equations we need to solve
constant-acceleration problems.
End of Lecture 2
!! Mastering
Physics
!! Before the next lecture, read the
text book, Chapters 2 and 3
!! Next lecture: Thursday, 1/15