Linear Motion
Or 1 Dimensional Kinematics
This problem was missed a lot
of 1314 benchmark. Did not
put in signs for calculation
A car is traveling west and
decreases its speed from 30 m/s
to 23 m/s in 2 seconds. What is
the car’s average acceleration?
Include direction.
9/9
 Goal:
Begin Motion
 Pick up Sample WS & calculator.
 Turn in Bubble Gum Lab to Sorter
 If you were absent, pick up the Bubble
Gum Lab from the mailbox. It will be
due Thursday.
 Tests are will be graded by tomorrow.
 Solve Now in dim. Analysis format:
 A starship travels at 6.5 x 108 m/sec.
How far does it travel in one day?
9/10 If absent Tue, get Sample
WS I
 Goal:
Calculate practice: distance,
displacement, speed and velocity
 Tests are graded. Missing: Taylor
Morgan,, Rina Rraci, Katana Shoemake,
Alexis Baldwin, Morgan Barrentine
 Solve Now:
 Thomas starts in a maze. He runs east
for 10 m and hits a dead end. He then
turns around and runs west for 15 m.
What distance did he run? What is his
displacement from his origin? Did he
run into any Grievers?
9/11




Have Linear Motion WS out to be checked
Pick up Acceleration WS and a calculator
Grades to date have been put in. There are quite a
few zeros  It is your responsibility to check
gradebook.
This was what was turned in last week
– Dim Analys WS (10 problems) due 9/2
– Tue 9/5 Sci Not practice due 9/2
– Safety Review due 9/4
– Sci Method Station due 9/5
– Bubble gum Lab due 9/8
– THIS WEEK ONLY, I will accept any of these
assignments today since I was out of town last
week.
Retests
 Scored
below 70 on original test
 Must come in and perform test
corrections before or after school
 Retests only after school
 You must sign up at least one day in
advance for a retake. You may not
do a retake if you have not done test
corrections.
 How
long does it take a motorcycle ,
initially at rest to increase its speed
to 15 m/s if it accelerates at
0.95m/s2?
 How many centigrams in a gram?
 How many meters in a kilometer?
Linear Motion
Great Website for Linear Motion
http://www.glenbrook.k12.il.us/gbssci
/phys/class/1DKin/U1L1a.html
Kinematics in one dimension
 the
study of linear motion (in a
straight line -not curved)
Motion
 What
does it mean for an object
to be in motion?
 It is the change in position of an
object as compared to a
reference point
*
Is the brick wall moving?
Not from where she’s sitting, but…
…from space, the earth rotates
and the wall with it.
So, whether or not something is moving
depends on your frame of reference.
*
Frame of Reference
a
fixed point used to determine
magnitude and direction of motion
 Magnitude?
 See Video Here
Rate
a
change in a given quantity over a
specified period of time (examples:
velocity and acceleration)
 What are some units of
measurement?
Scalar quantity
a
measurement
 Magnitude
 No direction implied
 Ex. mass, volume, density, distance,
speed
Vector quantity
a
measurement
 Magnitude
 Direction
 Ex.: displacement, velocity,
acceleration, force
Distance
 the
length of the actual path taken
by the object regardless of direction
 scalar quantity
 SI units include m, km
Displacement
 length
(measured in a straight line)
from the reference point to the
object (implies a given direction)
 Sometimes on graph labeled as
Position
 vector quantity
 SI units include m, km
Speed
 change
in distance divided by change
in time
 s =d/t
or v =d/t
 s is typically written “v”
 Where
– s = speed
– d = distance
– t = time
 scalar
quantity
 SI units include m/sec or cm/sec.
Velocity
 speed
in a given direction
 magnitude and direction included in
the measurement
 vector quantity
 SI units include m/sec or cm/sec.
 (v = ∆d/∆t) where
∆d= change in displacement (dfinal-dinitial)
∆t= change in time (tfinal-tinitial)
What is the unit for:
 Speed?
 m/s
 Velocity?
 m/s
 Acceleration?
 m/s2
What is the displacement for
Bob the Bear?
Dd = df – di
Dd = 90m – 20m = 70m
Displacement is not always equal to
distance travelled! What is Clyde the
Caterpillar’s displacement?
Dd = df – di
Dd = 80m – 20m = 60m
Sign for Vectors
 the
sign indicates direction
 can be positive or negative
 Right , East , or North are +
 Left, West, or South are -
What is the displacement for
Frank the Fish?
-70m
The negative sign tells us he is
moving opposite the direction of
the number line—in this case, to
the left.
Ex 1
 Travis
needs his physics notes. He
walks from his house 8 yards due
east towards Shannon’s house to
borrow her notes. At this point
Travis realizes he left his phone at
home and runs back to get it. After
picking up his phone he continues
the 14 yards east to Shannon’s
house. What was the distance and
displacement?
EX 1 Travis needs his physics notes. He walks from his house 8 yards
due east towards Shannon’s house to borrow her notes. At this point
Travis realizes he left his phone at home and runs back to get it. After
picking up his phone he continues the 14 yards east to Shannon’s house.
What was the distance and displacement?
Distance = 8yds + 8yds + 14 yds = 30 yds
Displacement = +8yds + -8yds + +14 yds =
+14 yds or 14 yds East
 The
Average Velocity
average velocity of an object is
defined as the displacement of an
object divided by the time in which it
took place.
*
Average velocity = Change in position
Change in time


vavg =
Dd
Dt
= d2-d1
t2-t1
Ex 2
A
racing car driven by Speed
E. Demon travels 480
kilometers in 2.0 hours.
Calculate the average speed
in km/hr and convert to m/s.
Ex 2 A racing car driven by Speed E. Demon travels 480 kilometers in 2.0
hours. Calculate the average speed in km/hr and convert to m/s.
Step 1
Step 3
List Variables
Show substitution (with units) and
d= 480 km
answer
v=?
v = 480 km= 240 km/hr
t = 2 hrs
2 hrs
Step 2
Show Formula
(arranged to solve for
unknown)
Step 4 This problem requires
v=d
dimensional analysis
t
240km 1000m 1hr
= 33.33 m/s
2 hr
1 km 3600s
Ex. 3
Sunday Driver takes her Cadillac
for a spin and travels 50.0 km
at an average speed of 35.0 m/s.
How long (in seconds) was she
driving her car?
1428.57 sec
Remember to change km to m!
t = d/v NOT dv
Sample 4
A car travels at a constant
speed of 4m/s for 5s. How far
does it go in m?
d = vt
20 m

Skip this year
A car travels at 60 km/hr for 200 km.
It then speeds up to 90km/hr and
travels an additional 200 km. What
is its average velocity?
Acceleration
 change
in velocity divided by change
in time (a = ∆v/∆t)
 Where


∆v = (vfinal-vinitial)
∆t =(tfinal-tinitial)
 vector
quantity
 SI units include m/sec2 or cm/sec2
*
Acceleration
Mathematically,
Avg
aavg
acceleration =
=
Dv
Dt
=
Change in velocity
Change in time
vf - vi
tf - ti
=
vf - vi
t
Ex 1
A
rocket takes off from rest
from the launching pad. It
accelerates to a speed of
150m/s during a time period
of 10 seconds. What was the
acceleration experienced by
the rocket?
Ex 1 A rocket takes off from rest from the launching pad. It accelerates to a
speed of 150m/s during a time period of 10 seconds. What was the
acceleration experienced by the rocket?
Step 1
List Variables
d=
vi = 0m/s (at rest)
vf = 150 m/s
a= ?
t = 10 sec
Step 2
Show Formula (rearranged)
a = vf – vi
t
Step 3
Show substitution (with units) and
answer
a = 150 m/s - 0m/s
10 sec
= 15 m/s2
Ex 2
Suppose
a treadmill has an
average acceleration of 4.7
m/s2. If the treadmill starts
at 1.7m/s, what would its
velocity be after 150
seconds?
Ex 2 Suppose a treadmill has an average acceleration of 4.7 m/s2. If the
treadmill starts at 1.7m/s, what would its velocity be after 150 seconds?
Step 1
List Variables
d=
vi = 1.7 m/s
vf = ?
a= 4.7 m/s2
t = 150 sec
Step 2
Show Formula (rearranged)
vf = vi + at
Step 3
Show substitution (with units) and
answer
vf = 1.7m/s + [(4.7 m/s2)(150 sec)
vf = 706.7 m/s
9/12 Get a calculator and blue
formula chart (by calculators). Solve
this now:
Practice Problem A
What
would the acceleration
of a car be if it goes from
100.0 m/s to 80.0 m/s in 5s?
Quiz
Today
after
warm
up!
Practice Problem A
What
would the acceleration
of a car be if it goes from
100.0 m/s to 80.0 m/s in 5s?
-4m/s2
Acceleration WS 1
3. A runner takes off from rest at the starting line. He
accelerates to a speed of 8.4 m/s during a time period
of 3.2 seconds. What was the acceleration of the
runner? 2.63 m/s2
4. A jet plane has an average acceleration of 23.8
m/s2. as it takes off from the ground. If it’s starting
velocity as it leaves the ground is 29.4 m/s, what
would its velocity be after 16 seconds? What would
the final velocity be in km/hr? 410.2 m/s
1476.72 km/hr
5. Don’t worry about this one yet
5. A boat is sitting still. The driver
starts the motor and accelerates at a
constant rate until he reaches a
velocity of 12.5 m/s 87 meters later.
How long does it take to achieve this
speed?
This is a 2 step problem.
Acceleration equations
 Remember
velocity, displacement,
and acceleration are all vector
quantities.
 Indicate direction
 right or east: positive
 left or west: negative
Finish Acceleration WS I #6-8
 vavg
= Δd/Δt
a
= Δv/Δt = vf – vi/t
a
= vf2 - vi2
2Δd
 Δd
= viΔt + ½aΔt2
 Δd
= viΔt + .5aΔt2
a – acceleration in m/s2
Dv - change in velocity in
m/s
vf – final velocity in m/s
vi – initial velocity in m/s
Dt or t – time interval in
seconds
d – displacement in m
Any of these formulas can be
rearranged!!!
 How
do we know which formulas to
use?
 DVVAT!!!!!
Example B
A
tricycle, initially traveling at 0.15 m/s,
experiences an acceleration of 0.045
m/s2.
 What is the velocity of such tricycle after
a period of 15 seconds?
vi = 0.15 m/s
a = 0.045 m/s2
t = 15 s
vf = ?
Example B
What equation?
vf = vi + aΔt
vf = 0.15 m/s +( 0.045 m/s2)(15 s)
vf = 0.83 m/s
Example C
A bowling ball decelerates. If it slows
from 15.3 m/s to 2.77 m/s in 14.0
seconds, what is the measure of
such deceleration?
vi = 15.3 m/s
vf = 2.77 m/s
t = 14.0 s
a=?
Example C
What equation?
vf = vi + aΔt
Solve for a
vf = vi + aΔt
vf - vi = aΔt
(vf – vi)/Δt = a
a = (2.77 m/s – 15.3 m/s)/(14.0 s)
a= -0.895 m/s2
Example D
An arrow takes a horizontal path the
arrow slows from 26.3 m/s to 15 m/s
during flight with an acceleration of
-0.83 m/s2 . How far does it travel?
vi = 26.3 m/s
vf = 15 m/s
a = -0.83 m/s2
d=?
Example D
What equation?
a=vf2 - vi2 / 2Δd
Solve for d
d=vf2 - vi2 / 2a
d = (15 m/s)2-(26.3m/s)2/(2 x-0.83 m/s2)
d= 281.14 m
9/12 Homework
Finish Acceleration WS I #6-8
How do we refer to a change in
speed or velocity?
What is acceleration?
 Can
you have constant speed and
still be accelerating?
 What is the formula for acceleration?
Hot Wheels Track
A boy is spinning on a merry-go-round
at constant speed of 0.5 m/s. Describe
his velocity. Describe his acceleration.
Acceleration summary
 Acceleration
is change in velocity
 Acceleration has magnitude and
direction
 If speed is constant, but the object is
changing direction, there is
acceleration
 When acceleration = 0, velocity is
constant
 If Acceleration is – and velocity is +,
the object is slowing down.
Vertical Acceleration
 Gravity
 This
 If
in a Vacuum
video is 3 min and 41 seconds
the link does not work, the name
is The Mechanical Universe: The Law
of Falling Bodies
 Show segment Gravity in a vacuum
Free Fall
In
the absence of air
resistance all objects dropped
near the surface of a planet
fall with the same constant
acceleration.
Free fall acceleration
 Also
called acceleration due to
gravity
 denoted with the symbol g.
 g = 9.8m/s2,
 since it is natural to fall down,
we will refer to the down
direction as +
 g = a = 9.8m/s2
Acceleration due to Gravity
 What
does it look like related to
speed?
If a ball was simply dropped
Freefall Practice Ex 14
Dylan
sits in a tree
dropping acorns on people
walking by. If the acorns
take 2.6 sec to hit the
ground, how tall is the tree
in which Dylan is sitting?
List your knowns! D-V-V-
d=?
vi = 0 m/s (0 VELOCITY
BEFORE IT DROPS!
vf
a = 9.8 m/s2 (Acceleration
due to gravity)
t = 2.6 sec
What
formula?
d = vit + .5at2
Remember since vi=0 vit=0
d = .5at2
d = (.5)(9.8m/s2)(2.6s)2
d = 33.1m
Practice Ex15

A flowerpot falls from a
windowsill 55.0m above
the sidewalk below.
1) How long do the people below
have to move out of the way?
2) How fast is the flowerpot going
when it hits the ground?
Practice Ex 16
Natalie is frustrated in Physics. She
throws her pencil downward with an
initial velocity of .68m/s. Her hand
is 80cm above the floor. What is
the velocity of the pencil in m/s
just before impact?
Brent is hanging over the
bleachers at a soccer game. He
opens his mouth to yell at
someone and his gum falls out
of his mouth straight down!!!!
What is the velocity of the gum
when it strikes the ground 15m
below?
 TEACHER
NOTES
 Describe the bet about catching a
dollar bill
 Have students measure a dollar bill
in cm and convert to m (I have some
cardboard ones)
Meter Stick Lab
Dollar Bill?
 Determine length and convert to meters
 Objective
Use g to determine your
reaction time and motor nerve conduction
speed
Materials
Meter Stick
Methods
1. Dropping and catching the meterstick.
 2. Start at zero
 3.Record distance of catch in centimeters
 4. Average 5 individual trials . Convert

MY DATA
 Dollar
bill 15.5 cm = .155m
 Average of 5 catches 32.4 cm =
.324 m
Determine your reaction time (t)
Let ag = 9.8 m/s2
ag simply means the acceleration due
to the force of gravity
Look at our velocity formulas. Do we
have enough information to solve for
time? List your D-V-V-A-T
Hint: what was the starting velocity of the
meterstick?
d = vit + .5at2 what is vit?
d = .5at2
Solve for t
t = √(d/.5a)
Calculate time
What else can we figure out
from this data?
 You
know the initial velocity of the
meter stick.
 What formula would you use to solve
for the vf?
 vf = vi + at
What goes up…
…must
come down!
What happens in terms of
velocity when a ball is thrown
into the air?
What happens in terms of
acceleration?
What is your reaction time
related to?
Determine the speed of motor neuron
conduction in m/s. What 2 values do
you need for speed?
Assume that the impulse in the motor
neuron traveled from the back of your
head to the tip of your index finger.
Thus, measure this distance to find d,
make sure you record this distance in
meters.
Solve for velocity of the impulse using
your reaction time and distance from
index finger to back of head.