Welcome to
Physics B
Trina Merrick
MCHS
*Slides/material thanks to
Dr. Peggy Bertrand of Oak Ridge High School, Oak Ridge,TN
Kinematics
Kinematics is the branch of mechanics
that describes the motion of objects
without necessarily discussing what
causes the motion.
 We will learn to describe motion in
two ways.

» Using graphs
» Using equations
Particle
A particle is an object that has mass
but no volume and occupies a position
described by one point in space.
 Physicists love to turn all objects into
particles, because it makes the math a
lot easier.

Position
How do we represent a point in space?
(x)

a) One dimension

b) Two dimensions (x,y)

c) Three dimensions (x,y,z)

Distance (d)
The total length of the path traveled
by a particle.
 “How far have you walked?” is a
typical distance question.
 SI unit:
meter (m)

Displacement (Dx)
The change in position of a particle.
 “How far are you from home?” is a
typical displacement question.
 Calculated by…
Dx = xfinal – xinitial
 SI unit:
meter (m)

Delta ( D )

D is a Greek letter used to represent
the words “change in”. Dx therefore
means “change in x”. It is always
calculated by final value minus initial
value.
Practice Problem
Question: If Dx is the displacement of a
particle, and d is the distance the
particle traveled during that
displacement, which of the following is
always a true statement?
a)
b)
c)
d)
e)
d = |Dx|
d < |Dx|
d > |Dx|
d > |Dx|
d < |Dx|
Practice Problem
A particle moves from x = 1.0 meter to
x = -1.0 meter.
a)
What is the distance d traveled by
the particle?
2.0 m
b)
What is the displacement of the
particle?
-2.0 m
Distance vs Displacement
B
100 m
displacement
50 m
A

distance
A picture can help you distinquish between
distance and displacement.
Practice Problem
You get on a ferris wheel of radius 20
meters at the bottom. When you reach
the top on the first rotation
what distance have you traveled?
b) what is your displacement from the bottom?
c) When you are on your way back down, does
the distance increase, decrease, or stay the
same? What about the displacement?
d) What is the distance traveled after you have
completed the full ride of 10 rotations? What
about the displacement?
a)
Practice Problem answers
You get on a ferris wheel of radius
20 meters at the bottom. When you
reach the top on the first rotation
a)
b)
d = ½ (2  r) =  r = 20  m
D x = 20 + 20 = 40 m
c) distance increases, displacement decreases
d)
d = 10 (2  r) = 400  m
Average Speed



How fast a particle is moving.
save = d
Dt
where:
save = rate (speed)
d = distance
D t = elapsed time
SI unit:
m/s
Average speed is
always a positive
number.
Average Velocity



How fast the displacement of a particle is
changing.
vave = ∆x
∆t
where:
vave = average velocity
Average velocity
∆x = displacement
is + or –
∆t = change in time
depending on
SI unit:
m/s
direction.
Demonstration
You are a particle located at the
origin.
 Demonstrate how you can move from x
= 0 to x = 10.0 with an average speed
of 0.5 m/s. You may not leave the xaxis!
 What was your average velocity in this
case?

Demonstration
You are a particle located at the point
x = 10.0 m.
 Demonstrate how you can move from x
= 10.0 to x = 0 with an average speed
of 0.5 m/s. You may not leave the xaxis!
 What is your average velocity in this
case?

Demonstration
You are a particle located at the
origin.
 Demonstrate how you can move from x
= 0 to x = 10.0 and back with an
average speed of 0.5 m/s. You may not
leave the x-axis!
 What was your average velocity in this
case?

Practice Problem
A car makes a trip of 1½ laps around a
circular track of diameter 100 meters
in ½ minute. For this trip
a) what is the average speed of the
car?
15.7 m/s
b) what is its average velocity?
3.33 m/s
Practice Problem
How long will it take the sound of the
starting gun to reach the ears of the
sprinters if the starter is stationed at
the finish line for a 100 m race?
Assume that sound has a speed of about
340 m/s.
Answer: 0.29 s
Practice Problem
x
t
Describe the motion of this
particle.
It is stationary.
Practice Problem
x
t
Describe the motion of this
particle.
It is moving at constant
velocity in the + x direction.
Practice Problem
x
B
A
Dx
Dt
vave = Dx/Dt
t
What physical feature of the
graph gives the constant
velocity?
The slope, because Dx/Dt is
rise over run!
Practice Problem
x (m)
Determine the
average velocity
from the graph.
Ans: 1/3 m/s
Force Concept Inventory
No scratch paper or calculator is necessary.
Use pencil on BLUE side of scantron sheet.
Name: Write your NAME followed by your TEST
NUMBER.
Subject: FCI
Date: 8/17/05
Period: ???
When you are done, bring your scantron sheet to the
front of the room and quietly begin working on
tonight’s homework.
Practice
Q 7: Is it possible for a car to circle a race track
with constant velocity? Can it do so with constant
speed?
Q 8: Friends tell you that on a recent trip their
average velocity was +20 m/s. Is it possible that
their instantaneous velocity was negative at any
time during the trip?
P 13: The human nervous system can propagate nerve
impulses at about 102 m/s. Estimate the time it
takes for a nerve impulse generated when your
finger touches a hot object to travel the length of
your arm. (HINT: How long is your arm,
Average Velocity Lab
Purpose: Figure out a way to make your cart move
with an average velocity of as close to 0.200 m/s as
possible. Use only the equipment provided. Photogate
must be in PULSE mode.
Tonight: Type your BRIEF and PARTIAL lab report.
The sections I want you to do are:
 Procedure
 Data (include a table of data for 5 trials, a
sample calculations, and a diagram of your
setup). Clearly indicate what you predicted
your average velocity to be, and what it
actually was during the demo.
Practice Problem
x
t
Does this graph represent motion
at constant velocity?
No, since there is not one constant
slope for this graph.
Practice Problem
x
A
vave = Dx/Dt
B
Dx
Dt
t
Can you determine average velocity
from the time at point A to the time
at point B from this graph?
Yes. Draw a line connecting A and B
and determine the slope of this line.
Practice Problem
Determine the
average velocity
between 1 and 4
seconds.
Ans: 0.17 m/s
Practice Problem
You drive in a straight line at 10 m/s
for 1.0 hour, and then you drive in a
straight line at 20 m/s for 1.0 hour.
What is your average velocity?
Answer: 15 m/s (this is probably what
you expected!)
Practice Problem
You drive in a straight line at 10 m/s
for 1.0 km, and then you drive in a
straight line at 20 m/s for another 1.0
km. What is your average velocity?
Answer: 13.3 m/s (this is probably NOT
what you expected!)
Always use the formula for average
velocity; don’t just take an “average” of
the velocities!
Instantaneous Velocity
The velocity at a single instant in
time.
 Determined by the slope of a
tangent line to the curve at a single
point on a position-time graph.

Instantaneous Velocity
x
vins = Dx/Dt
B
Dt
Dx
t
Draw a tangent line to the
curve at B. The slope of this
line gives the instantaneous
velocity at that specific time.
Practice Problem
Determine the
instantaneous
velocity at 1.0
second.
Ans: 0.85 m/s
Practice Problem
The position of a particle as a function
of time is given by the equation
x = (2.0 m/s) t + (-3.0 m/s2)t2.
a) Plot the x vs t graph for t = 0 until t =
1.0 s.
b) Find the average velocity of the
particle from t = 0 until t = 0.50 s.
c) Find the instantaneous velocity of the
particle at t = 0.50 s.
Practice
Q 10: If the position of an object is zero, does its
speed need to be zero?
Q 11: For what kind of motion are the
instantaneous and average velocities equal?
P 27: The position of a particle as a function of
time is given by x = (-2.0 m/s) t + (3.0 m/s2) t2.
a) Plot x-vs-t for time from t = 0 to t = 1.0 s.
b) Find the average velocity of the particle form t
= 0.15 s to t = 0.25 s.
c) Find the average velocity from t = 0.19 s to t =
0.21 s.
Acceleration (a)
Any change in velocity is called
acceleration.
 The sign (+ or -) of acceleration
indicates its direction.
 Acceleration can be…

» speeding up
» slowing down
» turning
Uniform (Constant) Acceleration
In Physics B, we will generally assume
that acceleration is constant.
 With this assumption we are free to use
this equation:

a = ∆v
∆t
 SI Unit:
m/s2
Acceleration has a sign!
If the sign of the velocity and the
sign of the acceleration is the same,
the object speeds up.
 If the sign of the velocity and the
sign of the acceleration are different,
the object slows down.

Practice Problem
A 747 airliner reaches its takeoff speed
of 180 mph in 30 seconds. What is its
average acceleration?
Practice Problem
A horse is running with an initial
velocity of 11 m/s, and begins to
accelerate at –1.81 m/s2. How long does
it take the horse to stop?
Practice Problem
v
t
Describe the motion of this particle.
It is moving in the +x direction at
constant velocity. It is not accelerating.
Practice Problem
v
t
Describe the motion of this
particle.
It is stationary.
Practice Problem
v
t
Describe the motion of this particle.
It starts from rest and accelerates in the
+x direction. The acceleration is constant.
Practice Problem
v
B
A
Dv
Dt
a = Dv/Dt
t
What physical feature of the
graph gives the acceleration?
The slope, because Dv/Dt is
rise over run!
Practice Problem
Determine the
acceleration from
the graph.
Ans: 10 m/s2
Practice Problem
Determine the
displacement of
the object from
0 to 4 seconds.
Ans: 0
Describe the
motion.
The object is initially moving in the negative direction at –20
m/s, slows gradually and momentarily is stopped at 2.0
seconds, and then accelerates in the + direction. At 4.0
seconds, it is back at the origin, and continues to accelerate in
the + direction.
Demonstration
Demonstration
Position vs Time Graphs


Particles moving with no
acceleration (constant velocity)
have graphs of position vs time
with one slope. The velocity is not
changing since the slope is
constant.
Position vs time graphs for
particles moving with constant
acceleration look parabolic. The
instantaneous slope is changing. In
this graph it is increasing, and the
particle is speeding up.
Uniformly Accelerating
Objects



You see the car move
faster and faster. This
is a form of
acceleration.
The position vs time
graph for the
accelerating car
reflects the bigger and
bigger Dx values.
The velocity vs time
graph reflects the
increasing velocity.
Position vs Time Graphs



This object is moving in the
positive direction and
accelerating in the positive
direction (speeding up).
This object is moving in the
negative direction and
accelerating in the negative
direction (speeding up).
This object is moving in the
negative direction and
accelerating in the positive
direction (slowing down).
x
Pick the constant velocity
graph(s)…
v
A
x
(This is not in the
notes.)
C
t
v
B
t
D
t
t
Draw Graphs for
Stationary Particles
x
v
a
t
Position
vs
time
t
Velocity
vs
time
t
Acceleration
vs
time
Draw Graphs for
Constant Non-zero Velocity
x
v
a
t
Position
vs
time
t
Velocity
vs
time
t
Acceleration
vs
time
Draw Graphs for Constant
Non-zero Acceleration
x
v
a
t
Position
vs
time
t
Velocity
vs
time
t
Acceleration
vs
time
Practice Problem
What must a particular Olympic
sprinter’s acceleration be if he is able to
attain his maximum speed in ½ of a
second?
In some problems, estimation is an
important part of the problem!
Practice Problem
A plane is flying in a northwest direction
when it lands, touching the end of the
runway with a speed of 130 m/s. If the
runway is 1.0 km long, what must the
acceleration of the plane be if it is to
stop while leaving ¼ of the runway
remaining as a safety margin?
Kinematic Equations
v = vo + at
» Use this one when you aren’t worried
about x.
 x = xo + vot + ½ at2
» Use this one when you aren’t worried
about v.
 v2 = vo2 + 2a(∆x)
» Use this one when you aren’t worried
about t.

Practice Problem
On a ride called the Detonator at Worlds
of Fun in Kansas City, passengers
accelerate straight downward from 0 to
20 m/s in 1.0 second.
What is the average acceleration of the
passengers on this ride?
b) How fast would they be going if they
accelerated for an additional second at this
rate?
c) Sketch approximate x-vs-t, v-vs-t and a-vs-t
graphs for this ride.
a)
Practice Problem
Air bags are designed to deploy in 10 ms.
Estimate the acceleration of the front
surface of the bag as it expands.
Express your answer in terms of the
acceleration of gravity g.
Practice Problem
You are driving through town at 12.0
m/s when suddenly a ball rolls out in
front of you. You apply the brakes and
decelerate at 3.5 m/s2.
How far do you travel before stopping?
b) When you have traveled only half the
stopping distance, what is your speed?
c) How long does it take you to stop?
d) Sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
a)
Practice problems

39. Landing with a speed of 115 m/s
and traveling due south, a jet comes
to rest in 7.00 x 102 m. Assuming the
jet slows with constant acceleration,
find the magnitude and direction of
its acceleration.
Practice problems
40. When you see a traffic light turn
red you apply the brakes until you
come to a stop. If your initial speed
was 12 m/s, and you were headed due
west, what was your average
acceleration during braking?
 41. Suppose the car in the previous
problem comes to rest in 35 m. How
much time does this take?

Practice problems

42. Starting from rest, a boat
increases its speed to 4.30 m/s with
constant acceleration
» (a) What was the boat’s average speed?
» (b) If it takes the boat 5.00 s to reach
this speed, how far has it traveled?
Practice problems

43. A cheetah accelerates from rest
to 25 m/s in 6.2 s. Assuming constant
acceleration,
» (a) how far has the cheetah run in this
time?
» (b) How far has the cheetah run in 3.1 s?
Lab Report Analysis
The
GOOD procedure
The BAD procedure
The UGLY procedure
The POETIC procedure
LAB REPORT FORMAT
Lab


The Physics 500
PartI: Determine your speed (use multiple
trials, etc.) while doing two activities using
a meterstick and stopwatch.
PartII: After choosing which of your
“activities” is more reliable, surrender your
meterstick and use you and your activity
speed to determine the unknown distance
marked off by your teacher.
Labs
Tumble Buggy Lab










TumbleBuggy Lab AP Physics
Constant Velocity
Devise a method to determine the speed of your TumbleBuggy.
Determine the Speed of the TumbleBuggy.
Devise a method to determine the length of the hall USING THAT
INFORMATION! The TumbleBuggy cannot, however enter the hallway. You also
MAY NOT measure the hallway with a meterstick!!
In the open area (hallway) devise a method to construct a table of data of position
versus time for your tumblebuggy. You are restricted to usingt he materials on the
materials table. All of them may not be needed. (Tape, paper, post-it notes, paper
clips)
Construct a Position vs. Time graph for the tumblebuggy.
Using information from that graph, determine the speed of the tumblebuggy.
Compare to the speed to the data from Part II.
Use that information to graph velocity versus time for the tumblebuggy. Determine
the acceleration from the graph.
Plot acceleration versus time for the tumblebuggy.
Lab






Picket Fence Lab
Purpose: To determine an approximate value for the
gravitational acceleration constant.
Theory: The gravitational acceleration constant, g, is
approximately 9.8 m/s2 near the surface of the earth.
Objects in free-fall therefore accelerate toward the earth
at a rate of 9.8 meters per second per second. The downward
instantaneous velocity of a freely falling object follows the
following equation: v = v0 - gt. If the instantaneous velocity
at various points during free-fall can be determined, the
gravitational acceleration constant should be able to be
estimated.
Equipment:
Photogate Stopwatch Meterstick “Picket Fence” CBL
Discussion: How did the acceleration you observe compare to
the actual acceleration due to gravity? What assumptions did
we make that could account for the differences? What are
some possible sources of human and equipment error?












Lab
Free
Fall
Times
Purpose: To investigate the relationship between the distance an
object falls from rest with the time it takes to travel that distance.
Theory: In the case of falling from rest, the second kinematic
equation
x = xo + vot + ½ a t2
can be use to derive the free fall equation
y = -1/2 g t2
where g is the acceleration due to gravity (9.8 m/s2), t is the time,
and y is the distance fallen.
Equipment: Photogate timers, droppable objects, meter sticks.
Procedure: Come up with a method to test the validity of the free
fall equation using the equipment given. Must include the dropping of
more than one type of object from several different heights.
Data and calculated results: Must appear in a clear and neat table,
and must include a comparison of calculated and measured results.
You might find the following equation handy:
% difference = measured result – theoretical result
theoretical result
Conclusion/Discussion: Should include problems encountered in
devising the procedure, a comparison of the free fall
characteristics of different objects (the same or different) and a
comparison of the calculated and measured results. Can you think of
any errors that you might have encountered and explain how these
errors might have affected your results?
Model problem (HW 44)

A kid slides down a hill on a toboggan
(a HAT?) with an acceleration of 3.0
m/s2. If he starts from rest, how far
has he traveled in
» (a) 1.0 s?
» (b) 2.0 s?
» (c) 3.0 s?
Model Problem (47)

Two car drive on a straight highway. At
time t = 0, car A passes mile marker 0
traveling due north with a speed of 28.0
m/s. At the same time, car B is 2.0 km
south of mile marker 0 traveling at 30.0
m/s due south. Car A is speeding up with an
acceleration of magnitude 1.5 m/s2, and car
B is slowing down with an acceleration of
magnitude 2.0 m/s2. Write x-vs-t equation
of motion for both cars.
Model Problem (48)

A 1-ton baby elephant jumps onto the
roof of a Volkswagon. Upon impact,
the elephant’s speed is 5.0 m/s. The
elephant makes a dent in the roof of
the Voltswagon that is 50 cm deep.
What is the magnitude of the
elephants deceleration, assuming it is
constant.
Model Problem (49)
Superman leaps into the air and moves
straight upward with constant
acceleration. After 5 seconds,
Superman has reached a height of
2,000 m.
 A) What is Superman’s acceleration?
 B) What is his speed at this time?

Model Problem (55)

A yacht cruising at 2.0 m/s is shifted
into neutral. After coasting 8.0 m, the
engine is engaged again and the yacht
resumes cruising at a reduced speed
of 1.5 m/s. How long did it take the
yacht to coast the 8.0 m?
Free Fall
Occurs when an object falls
unimpeded.
 Gravity accelerates the object toward
the earth the entire time it rises, and
the entire time it falls.
 a = -g = -9.8 m/s2
 Acceleration is always constant and
toward the center of the earth!!!

Symmetry in Free Fall




When something is thrown upward and
returns to the thrower, this is very
symmetric.
The object spends half its time traveling
up; half traveling down.
Velocity when it returns to the ground is
the opposite of the velocity it was thrown
upward with.
Acceleration is –9.8 m/s2 everywhere!
Demonstration
Object dropped from rest
 Object thrown up that falls.

Practice Problem
You drop a ball from rest off a 120 m
high cliff. Assuming air resistance is
negligible,
how long is the ball in the air?
b) what is the ball’s speed and velocity when it
strikes the ground at the base of the cliff?
c) what is the ball’s speed and velocity when it
has fallen half the distance?
d) sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
a)
Announcements
3/12/2016
Practice Problem
You throw a ball straight upward into
the air with a velocity of 20.0 m/s, and
you catch the ball some time later.
How long is the ball in the air?
b) How high does the ball go?
c) What is the ball’s velocity when you catch
it?
d) Sketch approximate x-vs-t, v-vs-t, a-vs-t
graphs for this situation.
a)
Pretest Free Response
A
h
Case 1: Ball A is dropped
from rest at the top of a
cliff of height h as shown.
Using g as the acceleration
due to gravity, derive an
expression for the time it
will take for the ball to hit
the ground.
Pretest Free Response
h
vo
B
Case 2: Ball B is projected
vertically upward from
the foot of the cliff with
an initial speed of vo.
Derive an expression for
the maximum height ymax
reached by the ball.
Pretest Free Response
A
h
vo
B
Case 3: Ball A is dropped
from rest at the top of the
cliff at exactly the same
time Ball B is thrown
vertically upward with
speed vo from the foot of
the cliff such that Ball B
will collide with Ball A.
Derive an expression for
the amount of time that will
elapse before they collide.
Pretest Free Response
A
h
vo
B
Case 4: Ball A is dropped
from rest at the top of the
cliff at exactly the same
time Ball B is projected
vertically upward with
speed vo from the foot of
the cliff directly beneath
ball A. Derive an expression
for how high above the
ground they will collide.