Announcements:
• Read preface of book for great hints on how to use the book to your
best advantage!!
• Labs begin Jan. 20 (buy lab manual).
• Bring ThinkPads to first lab (and some subsequent labs)!
• Questions about WebAssign and class web page?
• My office hours: MTWHF 1:00 pm - 2:00 pm, Olin 302.
• Pay attention to demos (may pop up in exams).
• Keep homework work sheets, etc (to prepare for exams).
• Keep a good, well-organized notebook (ppt slides, notes, homework)
TUTOR & HOMEWORK SESSIONS for Physics 113
This year’s tutors: Chad McKell, Xinyi Guo
Monday
Tuesday
Wednesday
Thursday
6-8 pm
6-8 pm
5:15 – 7:15
pm
6-8 pm
Chad
McKell
Chad
McKell
Xinyi Guo
Friday
Saturday
Sunday
Chad
McKell
All sessions will be in room Olin 103
Tutor sessions in past semesters were very successful and received high marks from students.
All students are encouraged to take advantage of this opportunity.
Chapter 2: Motion in One Dimension
Reading assignment: Chapter 2
Homework: OQ1, OQ17, OQ18, 1,4, 5,16, 18, 22, 29, 41, 58
(OQ – objective question, (concept) QQ – Quick quiz. Boxed problems are in student solution manual.)
Due dates:
Tu/Th section: Tuesday, Jan. 25
MWF section: Thursday, Jan. 27
Remember: Homework 1 due Jan. 18/Jan. 20.
• Kinematics: motion in terms of space and time (position, x; velocity, v; acceleration, a).
• We’ll mainly deal with constant acceleration.
• Derivatives: v 
dx
;
dt
a
dv
dt
• In this chapter we will only look at motion in one dimension.
Position,
Displacement and
distance traveled
Position: Location of particle with
respect to some reference point.
Displacement of a particle:
Its change in position:
x  x f  xi
xf final position
xi: initial position
Don’t confuse displacement with the distance traveled.
Example: What is the displacement and the total distance traveled of a baseball player
hitting a homerun?
Displacement is a vector: It has both, magnitude and direction!!
Total distance traveled is a scalar: It has just a magnitude
Velocity and speed
Average Velocity of a particle:
x
vx 
t
Average speed of a particle:
x: displacement of particle
t: total time during which displacement occurred.
total distance
average speed 
total time
Velocity is a vector: It has both, magnitude and direction!!
Speed is a scalar: It has just a magnitude
Blackboard example 2.1:
The position of a car is measured every
ten seconds relative to zero.
A) 30 m
B) 52 m
C) 38 m
D) 0 m
E) - 37 m
F) -53 m
Find the displacement, average velocity
and average speed between
positions A and F.
Instantaneous velocity and speed
x dx

t  0 t
dt
v x  lim
Instantaneous velocity is the derivative of x with respect to t, dx/dt!
Velocity is the slope of a position-time graph!
The (instantaneous) speed (scalar) is defined as the magnitude of its (instantaneous) velocity (vector)
10
Blackboard example 2.2
A particle moves along the x-axis.
Its coordinate varies with time
according to the expression:
x
(4 ms )  t
 (2 2 )  t
m
2
displacement (m)
8
6
4
x
2
0
t
-2
s
-4
0
0.5
1
1.5
2
2.5
3
3.5
time (s)
(a) Determine the displacement of the particle in the time intervals
t=0 to t=1s and t=1s to t=3s.
(b) Calculate the average velocity during these two time interval.
(c) Find the instantaneous velocity of the particle at t = 2.5s.
(d) i-clicker: What is the instantaneous velocity at 1s (graph)?
A.) 0 m/s B.) 0.5 m/s
C.) 1 m/s
D.) indeterminate
4
Acceleration
When the velocity of a particle (say a car) is changing, it is accelerating
(can be positive or negative).
The average acceleration of the particle is defined as the change in
velocity vx divided by the time interval t during which that
change occurred.
vx vxf  vxi
ax 

t
t f  ti
The instantaneous acceleration equals
the derivative of the velocity with respect to time (slope
of velocity vs. time graph).
v x dv x

t 0 t
dt Units: m/sec2
a x  lim
Because vx = dx/dt, the acceleration
can also be written as:
dvx d  dx  d 2 x
ax 
   2
dt dt  dt  dt
Worksheet:
Find the
appropriate
acceleration
graphs
parabola
Conceptual black board example 2.3
Relationship between acceleration-time graph and
velocity-time graph and displacement-time graph.
Notice that acceleration and velocity
often point in different directions!!!
One-dimensional motion with constant acceleration
v xf  v xi  a x t
*Velocity as function of time
x f  xi  (vxi  vxf )t
Position as function of time and velocity
1 2
x f  xi  v xi t  a x t
2
*Position as function of time
vxf  vxi  2ax ( x f  xi )
Velocity as function of position
1
2
2
2
Derivations: Book pp. 32-34
These four kinematic equations can be used to solve any problem
involving one-dimensional motion at constant acceleration.
Black board example 2.4
The driver of a car slams on the brakes when
he sees a tree blocking the road. The car
slows uniformly with an acceleration of –
5.60 m/s2 for 4.2s, making skid marks
62.4 m long ending at the tree. With what
speed does the car then strike the tree?
Freely falling objects
In the absence of air resistance, all objects fall towards the earth with
the same constant acceleration (a = -g = -9.8 m/s2), due to gravity.
i-clicker:
You throw a ball straight up in the air. At
the highest point, what are the velocity
and the acceleration of the ball
Galileo Galilei (1564-1642)
(from Wipipedia)
A.)
a=0;
v=0
B.)
a=-9.8m/s2
v≠0
C.)
a=-9.8m/s2
v=0
Black board example 2.5
A stone thrown from the top of a building is
given an initial velocity of 20.0 m/s
straight upward. The building is 50 m
high. Using tA = 0 as the time the stone
leaves the throwers hand at position A,
determine:
(a) The time at which the stone reaches its
maximum height.
(b) The maximum height.
(c) The time at which the stone returns to
the position from which it was thrown.
(d) The velocity of the stone at this instant
(e) The velocity and and position of the
stone at t = 5.00 s.
(f) Plot y vs. t; v vs. t and a vs. t
Review:
• Position x, velocity v, acceleration a
• Acceleration is derivative of v and 2nd derivative of x: a = dv/dt =
d2x/dt2, and v = dx/dt.
• Know x, v, a graphs. v is slope of x-graph, a is slope of v graph.
• Kinematic equations on page 36-38 (constant acceleration).
Know how to use!
• Free fall (constant acceleration)