Position -

Scalar - 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 Examples

Vector Diagrams 1D

Ex 1)

Distance = Displacement =

Speed = Velocity =

Ex 2)

Distance = Displacement =

Speed = Velocity =

Ex 3)

Distance = Displacement =

Speed = Velocity =

Ex 4)

Distance = Displacement =

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?

Time = 10s for all

Velocity Vectors…

Vector Diagrams 2D

Distance vs Displacement

Greater Distance: A B

Greater Displacement: A B

Q: If dA = 1500m and dB = 500m, how fast would A have to travel to reach peak at the same time as B?

Ex 1)

Pythagorean Theorem -

Trigonometry -

For each scenario, determine the resultants magnitude and direction…

Ex 2)

Dist =

Disp =

V =

Vector Components & Resultants…

Displacement Vectors Velocity VectorsA 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

Analytically: Analytically:

E

N

What is the magnitude and direction of the resultant velocity?

Position vs. Time• The x-axis is always “time”• The y-axis is always “position”• The slope of the line indicates the velocity of the object.• Slope = (y2-y1)/(x2-x1)

» d1-d0/t1-t0» Δd/Δt

Position vs. Time

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10

Time (s)Po

sitio

n (m

)

_______________ 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 graphsPosition vs. Time

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

Time (s)

Posit

ion

(m)

Position vs. Time

05

10152025

1 2 3 4 5 6 7 8 9 10Time (s)

Posit

ion

(m)

Position vs. Time

02468

1012141618

1 2 3 4 5Time (s)

Position vs. Time

02468

1012141618

1 2 3 4 5Time (s)

Velocity: _______ Acceleration: ______

Const Speed/Speeding Up/Slowing Down

Velocity: _______ Acceleration: ______

Const Speed/Speeding Up/Slowing Down

Velocity: _______ Acceleration: ______

Const Speed/Speeding Up/Slowing Down

Velocity: _______ Acceleration: ______

Const Speed/Speeding Up/Slowing Down

d

t

A

B

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 secDuring 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 Accelerationx

A …

B …

C …

D …

t

A

B C

D

+ Direction = North

Tangent Lines tell us ________________ Velocity

SLOPE VELOCITYPositive NegativeZero

SLOPE SPEEDFastGentle Zero

t

x

Determing Direction

t

x

Put an ‘X’ at the point when the object changes direction

Concavity

t

x

On a position vs. time graph:Concave up means ______________acceleration.Concave down means _____________acceleration.

Special Points

Inflection Pt. P, R Change of concavity, change of________________Peak or Valley QTime Axis Intercept P, S

t

x

PQ

R

S

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• X-axis is the “time”

• Y-axis is the “velocity”

• Slope = ___________

Velocity vs. Time

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10

Time (s)

Velco

ity (m

/s)

Different Velocity-time graphsVelocity vs. Time

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10

Time (s)

Veloc

ity (m

/s)

Velocity vs. Time

05

10152025

1 2 3 4 5 6 7 8 9 10

Time (s)

Veloc

ity (m

/s)Velocity vs. Time

02468

1012141618

1 2 3 4 5Time (s)

Velocity vs. Time

02468

1012

1 2 3 4 5Time (s)

Velocity vs. Time• Horizontal lines = _______________• Sloped line = ___________________• Steeper = greater change in _________ per second

• Remember that velocity =• Rearranging, we get Δx = • So….the area underneath a velocity-time graph is equal to…

Area Underneath v-t Graph

Determine the Displacement for each graph…

v

t

t

x

Area Underneath v-t Graph

Estimate the net displacement (Δx) for the graph above.Sketching the motion on the position-time graph below.

Acceleration vs. Time• Time is on the x-axis• Acceleration is on the y-axis• Shows how acceleration changes over a period of time.• Often a horizontal line.

Acceleration vs. Time

0

2

4

6

8

10

12

1 2 3 4 5 6 7 8 9 10

Time (s)

Acce

lerati

on (m

/s^2)

dt

vt

Translate the Displacement-Time Graph to Velocity-Time Graph

Kinematics 1D -

Motion : ____________________________________________________________________

Types of Motion Ticker Tape Diagram Motion Graphs

d

t

v

t

d

t

v

t

d

t

v

t

d

t

v

t

Slope = Slope =

Motion Graphs

Displacement vs Time (d vs. t) Velocity vs. Time (v vs. t) Slope = Slope =

Area =

d v

t t

A- At restB – Slow const velocityC – Fast const velocityD – Speeding UpE – Slowing down

Acceleration vs Time (a vs. t)

a

t

a

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

Average Velocity:

Q1: What is the average velocity of the marble?

Q2: Was the marble moving at constant velocity?

Q3: What was the final velocity of the marble?

“A marble starts from rest and rolls down a 1.5m incline in ______s “…

Acceleration:

Q4: What was the acceleration of the marble?

Distance Formula:

Q5: Confirm that the marble rolled 1.5m.

Final Velocity Formula:

Q6: Confirm the final velocity.

Horizontal Kinematics: A car ride

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?

d

t

v

t

The car then cruises at a constant velocity for 1000m…

Q3) How long did it take to travel this distance?

The car then slams on the breaks coming to a skidding stop in 10m…

Q4) What was the deceleration of the car?

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) Displacement (m)

Equation used Equation used

0

1

2

3

4

5

6

7

8

Q1) At what rate does the space ship gain speed?

Q2) Draw a ticker tape diagram of the space ships motion.

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 200m 300m 400 500m 600m

v 0 = v 1 = v 2 = v 3 = v 4= v 5 = v 6 = v 7 = v 8 =

Q) How far did the space ship go between the time interval 4 and 8 seconds?

Displacement vs Time Velocity vs Time 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

Beliefs on Motion Beliefs on Motion

Lived When? Lived When?

Lived Where? Lived Where?

Profession… Profession…

Vertical Kinematics- Free Fall Motion“Neglecting air friction!!!!”

a

Dropped from rest, what velocity does an object have after falling…

1s…

2s…

3s…

4s…

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?

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 ) II) Displacement ( d ) Given Time No Timevi = 0 vi= 0t = 7.5s d = 276m

Given Time No Timevi = 0 vi= 0t = 10s vf = 98.1m/s

Given Distance Given Speedvi = 0 vi= 0d = 40m vf = 28m/s

Given Givenvi = 0 vi= 0d = 7.29m vf = 4.86m/st = 3s t = 3s

III) Time ( s ) IV) Acceleration ( a => g )

“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?

g) If the ball reached 50m high, what velocity was it shot with?

BIG IDEAS

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 situationsDuring 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…

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?

Q1: How long until the fathers camera hits the ground?