Physics 114A - Mechanics
Lecture 3 (Walker: 2.4-5)
Velocity & Acceleration
January 6, 2011
John G. Cramer
Professor Emeritus, Department of Physics
B451 PAB
jcramer@uw.edu
Announcements
 Homework Assignments #1 is now available on WebAssign
and is due at 11:59 PM on Thursday, January 12.
Assignment #2 is also posted and is due at 11:59 PM on
Thursday, January 19. So far 172/216 WebAssign accounts.
 Obtain a H-iTT clicker from the University Bookstore. We
will begin using them for credit next Monday. RF Clickers
should be set to Channel 01. Register your clicker using the
“Clicker” link on the Physics 114A Syllabus page. So far
121/216 clickers are registered.
 On January 20 we will have Exam 1. It will be 75% multiple
choice and 25% free response. There will be assigned
seating. If would like a left-handed seat, an aisle seat, or a
front-row seat, send me E-mail with your preference.
January 6, 2012
Physics 114A - Lecture 3
2/19
Lecture Schedule (Part 1)
Physics 114A - Introduction to Mechanics - Winter-2012
Lecture: Professor John G. Cramer
Textbook: Physics, Vol. 1 (UW Edition), James S. Walker
Week
1
2
3
Date
L#
Slides
Reading
2-Jan-12
H1
3-Jan-12
1
Introduction to Physics
12
21
Chapter 1
5-Jan-12
2
Position & Velocity
8
22
2-1 to 2-3
6-Jan-12
3
Velocity & Acceleration
10
25
2-4 to 2-5
9-Jan-12
4
Equations of Motion
9
20
2-6 to 2-7
10-Jan-12
5
Vectors
8
24
3-1 to 3-3
12-Jan-12
6
r, v & a Vectors
5
24
3-4 to 3-5
13-Jan-12
7
Relative Motion
3
18
3-6
16-Jan-12
H2
17-Jan-12
8
2D Motion Basics
5
19
4-1 to 4-2
19-Jan-12
9
2D Examples
13
22
4-3 to 4-5
20-Jan-12
E1
January 6, 2012
Lecture Topic
Pages
HW Due
Lab
New Year Holiday
No Lab 1st week
No HW
We are here.
1-D Kinematics
HW1
MLK Birthhday Holiday
Free Fall & Projectiles
HW2
EXAM 1 - Chapters 1-4
Physics 114A - Lecture 3
3/19
Velocity &
Acceleration
Graphical Interpretation of
Average & Instantaneous Velocity
January 6, 2012
Physics 114A - Lecture 3
5/19
Velocity & Slope
The position vs. time graph of a particle moving
at constant velocity has a constant slope.
4.5 m
The position vs. time graph
of a particle moving with a
changing velocity has a
changing slope.
January 6, 2012
3.0 s
slope = velocity = 4.5 m/3.0 s = 1.5 m/s
Physics 114A - Lecture 3
6/19
Constant Acceleration
Acceleration characterizes
the change in velocity with time:
v/t.
If the acceleration is
constant, then the velocity is
changing at a constant rate.
Graphically, if we plot the
velocity vs. time, it will fall on a
straight line with a slope
determined by the acceleration.
vx  v0 x  v  v0 x  aav x t
ax  aav x if ax is constant
January 6, 2012
Physics 114A - Lecture 3
7/19
Acceleration
Average acceleration:
aav , x
vx v fx  vix


t
t f  ti
(so vx  aav , x t)
Instantaneous acceleration:
v x
ax (t )  lim
 t  0 t
Acceleration units: (m/s)/s = m/s2
January 6, 2012
Physics 114A - Lecture 3
8/19
Position, Velocity, & Acceleration
Velocity positive;
acceleration zero.
Velocity negative;
acceleration negative.
Velocity positive;
acceleration
negative.
Velocity zero;
acceleration zero.
Velocity positive;
acceleration positive.
January 6, 2012
Physics 114A - Lecture 3
9/19
Acceleration
Average acceleration:
Eqn. (2-5)
January 6, 2012
Physics 114A - Lecture 3
10/19
Acceleration
Graphical Interpretation of Average and
Instantaneous Acceleration:
January 6, 2012
Physics 114A - Lecture 3
11/19
Example: An Accelerating Train
A train moving in a straight line
with an initial velocity of 0.50 m/s
accelerates at 2.0 m/s2 for 2.0 s,
coasts with zero acceleration for
3.0 s, and then accelerates at -1.5
m/s2 for 1.0 s.
(a) What is the final velocity vf of
the train?
(b) What is the average acceleration
aav of the train?
v f  vi  v  vi  a1t1  a2 t2  a3t3
 (0.50 m/s)  (2.0 m/s 2 )(2.0 s)  (0 m/s 2 )(3.0 s)  (1.5 m/s 2 )(1.0 s)
 3.0 m/s
v v f  vi (3.0 m/s)  (0.5 m/s)
aav 


 0.42 m/s 2
t t f  ti
(6.0 s)  (0 s)
January 6, 2012
Physics 114A - Lecture 3
12/19
Acceleration vs. Deceleration
Acceleration (increasing speed) and deceleration
(decreasing speed) should not be confused with
the directions of velocity and acceleration:
Decelerating
Accelerating
Decelerating
January 6, 2012
Accelerating
Physics 114A - Lecture 3
13/19
Motion with Constant Acceleration
If the acceleration is constant, the velocity
changes linearly:
(2-7)
Slope Constant
Slope Changing
vav  12 (v0  v)
Changing
Acceleration
Constant
Acceleration
January 6, 2012
Physics 114A - Lecture 3
14/19
Motion with Constant Acceleration
Velocity vs. time:
(2-7)
Average velocity:
(2-9)
Position as a function of time:
(2-10)
(2-11)
Velocity as a function of position:
(2-12)
January 6, 2012
Physics 114A - Lecture 3
15/19
Motion with Constant Acceleration
The relationship between position and time
follows a characteristic curve.
Parabola
January 6, 2012
Physics 114A - Lecture 3
16/19
Motion with Constant Acceleration
January 6, 2012
Physics 114A - Lecture 3
17/19
Example: Hit the Brakes!
A park ranger driving at 11.4 m/s in
back country suddenly sees a deer
“frozen” in the headlights. He applies
the brakes and slows with an
acceleration of 3.80 m/s2.
(a) If the deer is 20.0 m from the
ranger’s car when the brakes
are applied, how close does
the ranger come to hitting
the deer?
(b) What is the stopping
time?
v 2  v02 (0)2  (11.4 m/s)2
d  20.0 m 17.1 m  2.9 m
x 

 17.1 m
2
2a
2(3.80 m/s )
v0
(11.4 m/s)
v  v0  at  0  t    
 3.00 s
2
a
(3.80 m/s )
January 6, 2012
Physics 114A - Lecture 3
18/19
End of Lecture 3
 Before Monday, read Walker Chapter 2.6 and 2.7.
 Register for WebAssign to do homework (so far,
172/216). Homework Assignments #1 is now available
on WebAssign. Assignment #1 is due at 11:59 PM on
Thursday, January 12. Assignment #2 is also posted
and is due at 11:59 PM on Thursday, January 19.
 Obtain a H-iTT clicker from the University
Bookstore. We will begin using them for credit next
Monday. RF Clickers should be set to Channel 01.
Register your clicker using the “Clicker” link on the
Physics 114A Syllabus page (so far 121/216
registered). We’ll test them now.