Position -
Scalar -
Examples
Vector -
Distance-
Displacement : Δd = df – di
Speed -
Velocity-
A baseball player hits a homerun. It is 90ft to each base and
the batter rounds the bases ending back at home plate…
Q: What was the batters distance traveled and total displacement?
Examples
Vector Diagrams 1D
Time = 10s for all
Ex 1)
Ex 2)
Distance =
Displacement =
Distance =
Displacement =
Speed =
Velocity =
Speed =
Velocity =
Ex 3)
Ex 4)
Distance =
Displacement =
Distance =
Displacement =
Speed =
Velocity =
Speed =
Velocity =
Can distance and displacement be the same thing? If so, then when and what does that mean for
speed and velocity under the same conditions?
Velocity Vectors…
Vector Diagrams 2D
For each scenario, determine the resultants magnitude and direction…
Distance vs Displacement
Ex 1)
Dist =
Disp =
Ex 2)
Greater Distance:
A
Greater Displacement:
B
A
V=
B
Q: If dA = 1500m and dB = 500m, how
fast would A have to travel to reach
peak at the same time as B?
Pythagorean Theorem -
Trigonometry -
Vector Components & Resultants…
Displacement Vectors
Velocity Vectors
A dog runs 50m @ 40⁰ North of East..
A plane flies East at 100m/s while a wind blows
North at 50m/s..
What are the x and y components?
What is the resultant velocity of the plane?
Graphically:
Using a scale of 1cm = 10m
Graphically: Using a scale of 1cm = 25m/s
N
E
Analytically:
Analytically:
What is the magnitude and direction of the resultant velocity?
Position vs. Time
Position vs. Time
• The x-axis is always “time”
20
18
• The y-axis is always “position”
16
• The slope of the line indicates the
velocity of the object.
Position (m)
14
12
10
8
6
• Slope = (y2-y1)/(x2-x1)
» d1-d0/t1-t0
» Δd/Δt
4
2
0
1
2
3
4
5
6
Time (s)
7
8
9
10
_______________ Diagram…Strobe pictures reveal the position of the object at
regular intervals of time, in this case, once each 0.1 seconds.
Notice that the ball covers an equal distance between flashes. Let's assume this
distance equals 20 cm and display the ball's behavior on a graph plotting its x-position
versus time.
• Slope is related to Velocity
• Steep slope = _____________
• Shallow slope = ___________
Different Position. Vs. Time graphs
Position vs. Time
Position (m)
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
Ti me (s)
Velocity: _______ Acceleration: ______
Velocity: _______ Acceleration: ______
Const Speed/Speeding Up/Slowing Down
Const Speed/Speeding Up/Slowing Down
Position vs. Time
Position (m)
25
20
15
10
5
0
1
2
3
4
5
6
7
8
9
Ti me (s)
10
Velocity: _______ Acceleration: ______
Velocity: _______ Acceleration: ______
Const Speed/Speeding Up/Slowing Down
Const Speed/Speeding Up/Slowing Down
d
B
A
t
C
A…
B…
C…
A) 0 to 2 sec B) 2 to 5 sec C) 5 to 6 sec D) 6 to 7 sec E) 7 to 9 sec F)9 to 11 sec
During which intervals was he traveling in a positive direction?
During which intervals was he traveling in a negative direction?
During which interval was he resting in a negative location?
During which interval was he resting in a positive location?
During which two intervals did he travel at the same speed?
Graphing Acceleration
x
+ Direction = North
B
C
t
A
A…
B…
C…
D…
D
Tangent Lines tell us ________________
Velocity
x
t
SLOPE
VELOCITY
SLOPE
Positive
Fast
Negative
Zero
SPEED
Gentle
Zero
Determing
Direction
Put an ‘X’ at the point when the object changes
direction
x
t
Concavity
x
t
On a position vs. time graph:
Concave up means ______________acceleration.
Concave down means _____________acceleration.
Special Points
x
Q
R
P
S
Inflection Pt.
P, R
Peak or
Valley
Q
Time Axis
Intercept
P, S
Change of concavity,
change of________________
t
Graphing Velocity in One Dimension
• Determine, from a graph of velocity versus
time, the velocity of an object at a specific
time
• Determine the acceleration from a velocity
vs time graph
• Calculate the displacement of an object from
the area under a v-t graph
Velocity vs. Time
Ve locity vs. Time
20
• X-axis is the “time”
18
16
• Y-axis is the
“velocity”
Velcoity (m/s)
14
12
10
8
6
• Slope = ___________
4
2
0
1
2
3
4
5
6
Time (s)
7
8
9
10
Different Velocity-time graphs
Velocity (m/s)
Velocity vs. Time
20
15
10
5
0
1
2
3
4
5
6
7
8
9
10
7
8
9
10
Time (s)
Velocity (m/s)
Velocity vs. Time
25
20
15
10
5
0
1
2
3
4
5
6
Time (s)
Velocity vs. Time
• Horizontal lines = _______________
• Sloped line = ___________________
• Steeper = greater change in _________
per second
Area Underneath v-t Graph
• Remember that velocity =
• Rearranging, we get Δx =
• So….the area underneath a velocity-time
graph is equal to…
Determine the Displacement for each graph…
Area Underneath v-t Graph
v
t
Estimate the net displacement (Δx) for the graph above.
Sketching the motion on the position-time graph below.
x
t
Acceleration vs. Time
Acceleration vs. Time
• Time is on the x-axis
• Shows how acceleration
changes over a period of
time.
• Often a horizontal line.
10
Acceleration (m/s^2)
• Acceleration is on the yaxis
12
8
6
4
2
0
1
2
3
4
5
6
Time (s)
7
8
9
10
Translate the Displacement-Time Graph to Velocity-Time Graph
d
t
v
t
Kinematics 1D -
Motion : ____________________________________________________________________
Types of Motion
Ticker Tape Diagram
Motion Graphs
Slope =
Slope =
d
v
t
d
t
v
t
d
t
v
t
d
t
v
t
t
Motion Graphs
Displacement vs Time (d vs. t)
Slope =
Velocity vs. Time (v vs. t)
Slope =
Area =
A- At rest
B – Slow const velocity
C – Fast const velocity
D – Speeding Up
E – Slowing down
d
v
t
t
Acceleration vs Time (a vs. t)
a
a
t
t
The Kinematics Equations…
Analyze – underline important and relevant
information. (quantities, direction etc)
Given/Find – list the given and find information
to help determine which equation to use
Equation – write down the equation necessary to
solve the problem
Algebra – use algebra (if necessary) to isolate the
variable you are solving for
Substitution – fill the given quantities into the
equation WITH UNITS!!!!!!
Answer – label your answer WITH UNITS and box in
Using the Kinematics Equations
“A marble starts from rest and rolls
down a 1.5m incline in ______s “…
Average Velocity:
Acceleration:
Q1: What is the average velocity of the marble?
Q4: What was the acceleration of the marble?
Q2: Was the marble moving at constant velocity?
Distance Formula:
Q5: Confirm that the marble rolled 1.5m.
Q3: What was the final velocity of the marble?
Final Velocity Formula:
Q6: Confirm the final velocity.
Horizontal Kinematics: A car ride
The car then cruises at a constant velocity for 1000m…
Q3) How long did it take to travel this distance?
d
t
The car then slams on the breaks coming to a skidding
stop in 10m…
v
Q4) What was the deceleration of the car?
t
A car accelerates from rest at a constant rate of 2m/s2 for
10s in the positive direction…
Q1) What is the final velocity after 10s?
Q2) How far did the car go during this time?
Q5) How long did it take to come to a stop?
Q6) What was the average velocity of the car during breaking?
Uniform Accelerated Motion: A Rocket
A rocket ship in outer space sits motionless at rest. The engines
ignite and the ship accelerates uniformly. After accelerating
for 5s, the spaceship is traveling at 100m/s…
Time (s)
Velocity(m/s)
Equation used
0
1
Displacement (m)
Q1) At what rate does the space ship
gain speed?
Equation used
Q2) Draw a ticker tape diagram of
the space ships motion.
2
3
4
5
6
7
8
Q3) Complete the data chart..
Q4) Does the spaceship move the
same distance for each given second?
Explain..
Directions: Fill in the values for the velocity at each time. Then draw the ship at its approximate
location for each time and note the time next below the ship
0m
100m
Displacement vs Time
200m
300m
400
500m
Velocity vs Time
Q) How far did the space ship go between the time interval 4 and 8 seconds?
600m
Acceleration vs Time
Problem Solving Using Kinematics Equations
A marble is given a push so that it rolls up an incline. The marble was given an
initial velocity of 4m/s and rolls 2m in 1.2s. Assuming that ‘up the incline’ is
considered the (+) direction. Determine the acceleration of the marble.
BONUS: What angle must the incline be set at?
(Hint: Acceleration is a vector)
Motion of Falling Bodies: Aristotle vs Galileo
Aristotle : Biography
Galileo: Biography
Lived When?
Lived When?
Lived Where?
Lived Where?
Profession…
Profession…
Beliefs on Motion
Beliefs on Motion
Vertical Kinematics- Free Fall Motion
“Neglecting air friction!!!!”
A rock is dropped off of a cliff 100m tall..
Q1) How long until the rock hits the ground?
Q2) How fast does it hit the ground?
a
Dropped from rest, what velocity does
an object have after falling…
1s…
2s…
3s…
4s…
Q3) How fast would rock hit ground if it was thrown
downward at 5m/s?
Free Fall – What can be asked and what to use….
I) Velocity ( v )
Given Time
vi = 0
t = 7.5s
II) Displacement ( d )
No Time
vi= 0
d = 276m
III) Time ( s )
Given Distance
vi = 0
d = 40m
Given Time
vi = 0
t = 10s
No Time
vi= 0
vf = 98.1m/s
IV) Acceleration ( a => g )
Given Speed
vi= 0
vf = 28m/s
Given
vi = 0
d = 7.29m
t = 3s
Given
vi= 0
vf = 4.86m/s
t = 3s
“Its easy estimate how fast an object falls
for a given amount of time”
Do Now:
a) At what time is the acceleration the greatest?
b) Explain what it means to accelerate at 9.81m/ss.
c) In what document can you find this constant?
d) From past discussions, at what time does the
distance an object falls and the velocity have the
same numerical value?
e) Estimate (using g=10)how fast an object is
moving after falling for 15s?
f) Now calculate the exact speed an object has
after falling for 15s.
g) How far will an object fall after 15s?
Free Fall – Objects thrown upwards….
A ball is shot upwards with an initial velocity of 25m/s…
a) How long until it reaches its maximum height?
b) What is the acceleration at its maximum height? _____________
c) What is the velocity at its maximum height? _________________
d) How high does the ball reach? Aka…
e) Name 2 times that ball is at same height. _________&__________
f) What is the velocity at each of these times?
BIG IDEAS
g) If the ball reached 50m high, what velocity was it shot with?
A ball is thrown upward with a speed of 38 m/s from the
edge of a cliff of height h = 10 m. How long does it take to
fall to the bottom of the cliff?
Free Fall – More complex situations
During the shooting of a zombie apocalypse movie, a stunt is to be performed where a
stranded character on a rooftop jumps and miraculously lands safely in a convertible rescue
car that is moving.
Q1: If the building is 15m high and the rescue car is a
horizontal distance of 20m away from the landing point
moving at a constant speed, how fast must the car be
moving to catch the (stunt dummy)?
Q2: If it takes .15s for the stunt dummy to come to rest from the moment it contacts the soft cushioned seat until its
vertical velocity reaches zero, how many g’s does the stunt dummy experience? Why wouldn’t a ‘real’ human perform
this stunt?
Free Fall – Extra Credit
A man and his wife go for a ride in a hot air balloon. The balloon is rising into the sky at a
constant speed of 5m/s. The husband decides to take an aerial photo of his children below
when the balloon is 25m above the ground and accidentally drops his camera…
Q1: How long until the fathers camera hits the ground?
Q2: The son runs to catch the camera just before it hits the ground.
If the son was a horizontal distance of 10m away from where the
balloon lifted off, how fast does he have to run?