Good
Morning/
Afternoon
• Turn in: Graphs w/ analysis
• Get ready for some notes
• HW: pg. 78-79: 2-4, 9, 10; pg.
82: 1, 3, 6, 7, 14 (OpenStax
College Physics Book… the
one online)
KINEMATICS
Objects in motion…
Needed
Skills
• Right triangle trigonometry
• Unit Conversion
• Graph interpretation
ONE
DIMENSIONAL
MOTION
Classical
Mechanics
• Objects are large and move
relatively slow (v<<c)
• Consider all objects as
particles
– A particle is a point-like mass
having infinitesimal size and finite
mass.
• Objects do not rotate
S.I. Units
• Remember we have to use
proper S.I. (metric) units:
– Meters (m)
– Seconds (s)
– Kilograms (kg)
Kinematics
• Study of motion with no regard to
its causes.
• Objects move or do not move,
accelerate or do not accelerate
and we do not care why.
• First we’ll look at objects in
motion in one-dimension
• Later we’ll introduce twodimensional motion
Scalars vs.
Vectors
• Scalar – quantities with
magnitude (size) and units
• Vector – quantities with
magnitude (size), units, and
direction
Distance
• The distance of a particle is
defined as the total length of the
path traveled.
• Distance is SCALAR
– Always positive no matter which way
you move
• S.I. unit of meters (m)
Sample
An object moves from x = 2 m
to x = 5 m, stops and turns
around traveling then to x = -2
m. What is the total distance
the object travels?
Displacement
∆𝑥 = 𝑥𝑓 − 𝑥𝑜
Physicists consider
motion to the right
as positive and
motion to the left
as negative.
• The displacement of an object is
defined as its change in position.
• In other words, how far does it end up
from where it began?
– Change in anything is final - original
• Displacement is a VECTOR
– Depends on the direction relative to some
reference point.
• S.I. unit of meters (m)
Sample
An object moves from x = 2 m
to x = 5 m, stops and turns
around traveling then to x = -2
m. What is the total
displacement of the object?
Sample
A sprinter is to run the 400 m
dash. If the starting line is
where the finish line is, what is
the total distance the runner
travels and what is their
displacement?
Speed
• Average speed is defined as
𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠𝑝𝑒𝑒𝑑 =
𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒
• Speed is scalar so is always
positive
• S.I. derived unit of 𝑚/𝑠
Sample
A car travels 4000 m in 10 min.
What is the average speed of
the car?
Sample
Note: Since the distance,
time, and speed have
matching units we do
not need to convert
unless asked to.
A car is to travel 3000 km in 30 hrs.
If you complete the first 1500 km of
the trip averaging 75 km/hr, what
must be your average speed for the
second half of the trip?
Average
Velocity
𝑣𝑎𝑣𝑔
𝑣𝑎𝑣𝑔
∆𝑥
=
𝑡
𝑣𝑓 + 𝑣0
=
2
• Average velocity is defined as the
displacement of the object over
the time needed for the
displacement.
• Velocity is a vector so it required
direction.
• S.I. derived unit of 𝑚/𝑠
• The average velocity is truly
defined as the average of the final
and original velocities.
DIRT?
• Remember d=rt?
• Now its ∆𝑥 = 𝑣𝑡
–(avg. velocity equation)
Steps for Solving Rate Problems:
1. Diagram/Set-up reference point.
2.Set up equation(s).
3. Solve for unknowns.
Sample
Two locomotives approach each
other on parallel tracks. Each has a
speed of 95 km/hr with respect to
the ground. If they are initially 9.5
km apart, how long will it be before
they reach each other?
Sample
Dr. Sandomir is out for a morning walk in
the woods. A bear, 20 m behind him,
starts to give chase to Dr. Sandomir,
running at 3.0 m/sec. The fastest Dr.
Sandomir can run is 0.5 m/sec. If Dr.
Sandomir can JUST dive into his car as
the bear is catching up to him, how long
did it take the bear to catch him AND
how far was Sandomir from the car when
the bear gave chase?
Sample
A bowling ball traveling with constant
speed hits the pins at the end of a
bowling lane 16.5 m long. The bowler
hears the sound of the ball hitting the
pins 2.5 sec after the ball is released from
his hands. What is the speed of the ball?
The speed of sound is 340 m/sec.
Happy
Hump Day!
• Get out notes… let’s do this!
• Tomorrow: Constant Velocity Lab
• HW: Position Time Graphs WS
Position
Time
Graphs
Position
Time
Graphs
• The slope of a position time
graph:
–
𝑅𝑖𝑠𝑒
𝑟𝑢𝑛
–
𝑟𝑖𝑠𝑒
Units:
𝑟𝑢𝑛
=
∆𝑥
∆𝑡
= 𝑣𝑎𝑣𝑔
=
𝑚
𝑠
(units for velocity)
• Constant slope = constant velocity
• “Curved” (Parabolic) slope =
changing velocity
Sample
Given the graph to the left, determine
the following:
a) Total distance traveled and average
speed from A to G.
b) Average velocity for sections AB, BC,
CD, DE, EF, FG.
c) Average velocity from A to G.
Sample
a) Given the graph below, determine the
average velocity for the entire trip
from t = 0 – 5 seconds.
b) What direction is this object moving
in?
c) Is this object moving at a constant
velocity, speeding up, or slowing
down?
Throw Back
Thursday
• Make sure you turned in everything
from yesterday
• NOTE: If you need me at lunch I will be
in the Chemistry office in room 118.
Feel free to come find me.
• Stem Club Informational Meeting On
Tuesday after school
• Today we talk about ACCELERATION!
• HW: pg. 79: 13, 14, 17; pg. 80-81: 27,
30; pg. 82-83: 19, 22, 27, 32, 34
– Remember to use the PDF version!
Warm Up:
• Determine the average velocity in each
section.
• Determine the average velocity overall.
Accelerated
Motion
• Acceleration is defined as the rate
change in velocity:
∆𝑣 𝑣𝑓 − 𝑣𝑜
𝑎=
=
𝑡
𝑡
Since acceleration depends on the change
in velocity, one (or a combination) of the
following can cause can acceleration:
1. Speeding up in one direction
2. Slowing down in one direction
3. Changing direction at constant speed
Velocity
Time
Graphs
• The slope of a velocity time graph
represents…
• Slope of a velocity-time graph =
acceleration
• Unit analysis:
(𝑚/𝑠)/(𝑠) =
𝑚
𝑠2
(units for acceleration)
Velocity
Time
Graphs
• The area beneath a velocity time graph
represents…
• Unit analysis:
(𝑚/𝑠)(𝑠) = 𝑚
• Meters are a unit of displacement
• Area underneath velocity-time graph
= displacement
Velocity
Time
Graphs
True or false:
1.A car must have an
acceleration in the direction of
its velocity.
2.It is possible for a car to slow
down while having positive
acceleration.
Velocity
Time
Graphs
• Let’s analyze the graph at the left:
1
∆𝑥 = 𝑣𝑜 𝑡 + 𝑡 𝑣𝑓 − 𝑣𝑜
2
But
𝑣𝑓 − 𝑣𝑜
𝑎=
𝑡
So
1
∆𝑥 = 𝑣𝑜 𝑡 + 𝑡(𝑎𝑡)
2
1 2
∆𝑥 = 𝑣𝑜 𝑡 + 𝑎𝑡
2
Sample
A car is moving at 5.0 m/sec when it
accelerates at 2.0 m/sec2 for 3.5 sec.
Determine the final velocity of the car.
Sample
A car is moving at 5.0 m/sec when it
accelerates at 2.0 m/sec2 for 3.5 sec.
Determine the displacement of the car.
Sample
Use the graph to the right to answer the
following questions:
1. During which interval is the
acceleration the greatest?
2. During which interval is the object
moving the positive direction but
with a negative acceleration?
3. What is the final displacement of the
object?
Keep in mind:
1. If the object has the same sign on velocity
and acceleration, it is speeding up.
2. If the object has opposite signs on velocity
and acceleration, it is slowing down.
The
Timeless
Equation
• The timeless equation will be used if we are
given a problem without “time” information:
Start with:
1 2
∆𝑥 = 𝑣𝑜 𝑡 + 𝑎𝑡
2
Use:
𝑎=
2𝑎∆𝑥 =
2
𝑣𝑓
−
2
𝑣𝑜
𝑣𝑓 −𝑣𝑜
𝑡
∆𝑥 = 𝑣𝑜
but solve for “t”, 𝑡 =
𝑣𝑓 −𝑣𝑜
𝑎
Substitute “t”:
𝑣𝑓 − 𝑣𝑜
1 𝑣𝑓 − 𝑣𝑜
+ 𝑎
𝑎
2
𝑎
Simplify:
𝑣𝑓2 − 𝑣𝑜2
∆𝑥 =
2𝑎
2
Sample
A plane landing on an aircraft carrier hits
the deck at 250 m/sec and must stop in
275 m. What minimum acceleration must
the plane undergo?
Sample
A ball rolling down an incline is moving at
10 m/sec at one point and 3.0 m later is
moving at 15 m/sec.
a) What was the rate of acceleration
along the incline?
b) How much time did it take to travel
the 3.0 m?
c) If it continued this rate of acceleration
for one more second, how far would it
travel?