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Effort ArmResistance

Arm

Speed: A measure of motion, = distance divided by time. D/T

Copyright © 2010 Ryan P. Murphy



ScalarsNo Direction

Speed is the rate of motion, or the rate of change of position.



ScalarsNo Direction

Speed is the rate of motion, or the rate of change of position.

Can only be zero or positive.

Distance = Speed ● Time

D

S T


D

S T


X

÷÷

• How far did Joe walk if he walked a steady 4 km/h for three straight hours?



Distance = 4 km/h ● 3 h



Distance = 4 km/h ● 3 hDistance =



Distance = 4 km/h ● 3 hDistance = 12 km

D

S T

DistanceSpeed = --------------- Time

X

÷÷

• What is Joes speed if he walked a steady 5 km in one hour?

Rate / Speed R =

• What is Joes speed if he walked a steady 5 km in one hour?

Rate / Speed R = 5 km1 hour

or 5 km/hr

• What is Joes speed if he walked 5 km in one hour?

Rate / Speed R = 5 km1 hour

or 5 km/hr

• Juan travels 300km in 6hrs. Find his average speed in km/h.


• Speed = Distance / Time



300km• Speed = ------------ = 50 km/h

6h



300km 50km• Speed = ------------ = ---------

6h h

D

S T

DistanceTime = --------------- Speed

X

÷÷

• Marlene drove 500 km at an average speed of 50 km/h? How long did she drive?


• Time = Distance / Speed



500km • Time = ------------ = _____h

50km/h



500km • Time = ------------ = 10h

50km/h

Velocity = (distance / time) and direction.


• Velocity =–S is replaced with V because velocity is

speed and direction.


DV = ------

T

• What’s Joes velocity if he walked 4 kilometers East in one hour?

4 km East 4 km

• V = ----------- = 4 km/hr/east 1 hour


• What’s Joes velocity if he walked 4 kilometers East in one hour?

4 km East 4km km

• V = ----------- = 4 hr/east 1 hour


4kmhr

East

• Velocity deals with displacement.– Displacement measures where you end up

relative to where you started.


Start

Finish

4m

8m




Start

Now you try




Start




Start

Finish




Start

Finish

50m

60m

30m

100m




Start

Finish

50m

60m

30m

100m

178.88m

80m

• Find the displacement.


Start/Finish

Don’t try this one(It’s a trick)



Start/Finish

Try this one



Start/Finish

50m

50m 10m

10m

20m

100m

• The speed of the car is 80 km / hr .


• The velocity of the car is 80 km / hr / West.


• The velocity of the plane is 300 km / hr / West.



The speed of the plane is 300 km / hr


The speed of the plane is 300 km / hr

Speed and Velocity Calculations and problems. Learn more at…. http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-827.htm

http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-827.htm

http://www2.franciscan.edu/academic/mathsci/mathscienceintegation/MathScienceIntegation-827.htm

• It took Lightning McGreen 2.5 hours to travel 600 kilometers.–How fast was he going in Kilometers an

hour?


• Forces in Motion, Speed, Velocity, Acceleration and more available sheet.


hour?



hour?


Speed = Distance / Time


hour?


Speed = Distance / TimeSpeed = 600 km / 2.5 h


hour?


Speed = Distance / TimeSpeed = 600 km / 2.5 hSpeed = 240 km/h

• Answer: 240 km/h –Speed is distance over time.


• It took Ms. Rally 4 hours to travel 165 kilometers due North.–What was the velocity of her car in

Kilometers an hour?



Kilometers an hour?


V


Kilometers an hour?


VVelocity = Distance / Time


Kilometers an hour?


VVelocity = Distance / TimeVelocity = 165km / 4 h


Kilometers an hour?


VVelocity = Distance / TimeVelocity = 165km / 4 hVelocity = 41.25 km/h/North

• Answer: 41.25 km / h / North –Velocity is distance over time and

direction.


• What is the speed if the distance was 340 km and the time was 3 hours?–Was Jater speeding?




Speed = Distance / TimeSpeed = 340km / 3 h



Speed = Distance / TimeSpeed = 340km / 3 hSpeed = 113km/h

• 340 km / 3 hours = 113km/h–Jater was speeding.


• How far did Doc Budson travel if he was going 60 kilometers an hour for 4 straight hours?




Distance = Speed ● TimeDistance = 60km/h ● 4 h

• In this case, we just multiply the distance traveled by the time. 60 km/h times 4 hours.


• 60 km times 4 hours = 240 km–Check your work, 240/4 should be 60.


• What is the speed if a runner runs a distance of 400 meters in 43 seconds.




Speed = Distance / TimeSpeed = 400m / 43s



Speed = Distance / TimeSpeed = 400m / 43sSpeed = 9.30 m/s

• 400m / 43s = 9.30 m/s


• Activity! Looking for the Violators.


Safety is a big concern here. Students need to be far from road. Outside behavior must be excellent.


Safety is a big concern here. Students need to be far from road. Outside behavior must be excellent.

We also must try to conceal ourselves at all time. We do not want anyone to see us / slow down.

• Activity! Optional– Teacher measures out 300 feet along road and

puts a cone at the start and finish a short distance from the roads edge.

– From a distance, students use a stopwatch to time the speed of cars from the start cone to the finish cone.

– Speed = Distance (300 ft) divided by time (ft/sec.) – Multiply by .681 (ft/sec to mph conversion) = mph– Over 30 mph is speeding in the village.– Create list of all the speeds and then average.– Does the village have a speeding problem?



– From a hidden distance, students use a stopwatch to time the speed of cars from the start cone to the finish cone.

– Speed = Distance (300 ft) divided by time (ft/sec.) – Multiply by .681 (ft/sec to mph conversion) = mph– Over 30 mph is speeding in the village.– Create list of all the speeds and then average.– Does the village have a speeding problem?




– Speed = Distance (300 ft) divided by time (ft/s.) – Multiply by .681 (ft/sec to mph conversion) = mph– Over 30 mph is speeding in the village.– Create list of all the speeds and then average.– Does the village have a speeding problem?




– Speed = Distance (300 ft) divided by time (ft/s.) – Multiply by .681 (ft/sec to mph conversion) = mph– Over 30 mph is speeding in the village.– Create list of all the speeds and then average.– Does the town have a speeding problem?

Trains start off slow…

Example of Instantaneous velocity

• Note: This is nice to know.• Average vs. Instantaneous Velocity

– Instantaneous Velocity: When an object starts and then speeds up (not moving at one steady speed).



Instantaneous Velocity Definition: The velocity of an object at any given instant (especially that of an accelerating object); the limit of the change in position per unit time as the unit of time approaches zero; expressed mathematically



Instantaneous Velocity Definition: The velocity of an object at any given instant (especially that of an accelerating object); the limit of the change in position per unit time as the unit of time approaches zero; expressed mathematically

Note: Instantaneous Velocity of the shot

• Average: The result obtained by adding several quantities together and then dividing this total by the number of quantities; the mean

• Average: The result obtained by adding several quantities together and then dividing this total by the number of quantities; the mean.

Adding all the instantaneous velocities and then dividing this total by number of quantities

Acceleration = The rate of change in velocity. (m/s)


A = ----------------Velocity

Time

A = ----------------Velocity

Time

Delta (Means Change)

A = ----------------Velocity

Time


Or… a = (v2 − v1)/(t2 − t1)

• Acceleration is measured by taking the change in velocity of an object divided by the time to change that velocity:

A = ----------------Velocity

Time

• Video Link! Speed, Velocity, Acceleration– Be proactive, sketch problems in journal as

completed in video.– http://www.youtube.com/watch_popup?v=rZo

8-ihCA9E

http://www.youtube.com/watch_popup?v=rZo8-ihCA9E

http://www.youtube.com/watch_popup?v=rZo8-ihCA9E

Acceleration = The final velocity – the starting velocity, divided by time.


• Video Link (Optional) 100 meter final London Summer Games (Note Bolt’s acceleration)– http://www.youtube.com/watch?v=2O7K-8G2nwU

(Skip ahead to 4:15 for race)

http://www.youtube.com/watch?v=2O7K-8G2nwU

• Ratman's rat mobile is traveling at 80m/s North when it turns on its rocket boosters accelerating the rat mobile to 200 m/s in 4 seconds. – What’s the rat mobiles acceleration?




200 m/s 80 m/s

4 s



120 m/s

4 s


• The formula for acceleration is:• a = (Final velocity – starting velocity) / time.



• The formula for acceleration is:• a = (Final velocity – starting velocity) / time.• a = 200m/s -80m/s / 4 s =



• The formula for acceleration is:• a = (Final velocity – starting velocity) / time.• a = 200m/s -80m/s / 4 s =• a = 120 m/s / 4 s =



• The formula for acceleration is:• a = (Final velocity – starting velocity) / time.• a = 200m/s -80m/s / 4 s =• a = 120 m/s / 4 s = 30 m/s



• The formula for acceleration is:• a = (Final velocity – starting velocity) / time.• a = 200m/s -80m/s / 4 s =• a = 120 m/s / 4 s = 30 m/s North


Vector

• A car traveling at 10 m/s starts to decelerate steadily. It comes to a complete stop in 20 seconds. – What is its acceleration / deceleration?


a = (v2 − v1) t



a = (v2 − v1) t

0 m/s 10 m/s

20 s



a = (v2 − v1) t

10 m/s

20 s



a = (v2 − v1) t

10 m/s

20 s

- .5 m/s

• A unicyclist was traveling at 2 m/s South and speed up to 6 m/s in 3 seconds. – What was the acceleration?


• The final velocity (6 m/s) minus the starting velocity (2 m/s) South divided by the time (3 seconds) = acceleration.


6 m/s – 2m/s

3s – 0s



4 m/s

3s



4 m/s

3s

= 1.333 m/s South


Acceleration: Learn more at… http://www.physicsclassroom.com/class/1dkin/u1l1e.cfm

http://www.physicsclassroom.com/class/1dkin/u1l1e.cfm

http://www.physicsclassroom.com/class/1dkin/u1l1e.cfm

• Video Link! Khan Academy. Acceleration.• (Optional) complete problems as he does.

– Be active in your learning not passive.– http://www.khanacademy.org/science/physics/

mechanics/v/acceleration


http://www.khanacademy.org/science/physics/mechanics/v/acceleration

http://www.khanacademy.org/science/physics/mechanics/v/acceleration

Deceleration: To slow velocity.-


Deceleration: To slow velocity.Formula is the same as acceleration but

will be a negative value.


Deceleration: To slow velocity.Formula is the same as acceleration but

will be a negative value.


Note: There is no "deceleration", only negative acceleration

• The formula is the same, but the value will be a negative.–Deceleration = (final velocity – starting

velocity) divided by time.


• Lightning McGreen was traveling 200 m/s West when he slowed to 50 m/s in 10 seconds. –What was his deceleration?


• The final velocity (50 m/s) minus the starting velocity (200 m/s) divided by 10 seconds.


50 m/s - 200 m/s

10s – 0s



150 m/s

10s



150 m/s

10s

Deceleration = -15 m/s



150 m/s

10s

Deceleration = -15 m/s West



150 m/s

10s


Vector or Scalar?



150 m/s

10s


Vector



150 m/s

10s


Vector

M_______and d______



150 m/s

10s


Vector

Magnitudeand direction

Momentum: A measure of the motion of a body equal to the product of its mass and velocity.


Momentum = Mass * Velocity.


p = m v

Momentum = Mass * Velocity.


p = m vMomentu

mMass kg

Velocity m/s

• Momentum = ?


• Video Link! Momentum (Optional)– http://www.youtube.com/watch?v=edcpZoM5xmo


http://www.youtube.com/watch?v=edcpZoM5xmo

• What is the momentum of Fred if he weighs 3000 kg and is traveling with a velocity of 20 m/s / West?




p = m v



p = m vMomentum = 3000 kg 20/m/s/ West



p = m vMomentum = 3000 kg 20/m/s/ WestMomentum =



p = m vMomentum = 3000 kg 20/m/s/ WestMomentum = 60,000 kg/m/s West



p = m vMomentum = 3000 kg 20/m/s/ WestMomentum = 60,000 kg/m/s West

Can you put it into SI?



p = m vMomentum = 3000 kg 20/m/s/ WestMomentum = 60,000 kg/m/s WestMomentum = 6 x 104 kg/m/s West


• Momentum = 60,000 kg/m/s


Momentum. Learn more at… http://www.physicsclassroom.com/class/momentum/u4l1a.cfm

http://www.physicsclassroom.com/class/momentum/u4l1a.cfm

http://www.physicsclassroom.com/class/momentum/u4l1a.cfm

• Chick Licks weighs 1000 kg and had a velocity of 20 m/s North. –What was his momentum?




p = m v



p = m vMomentum = 1000 kg 20/m/s/ North



p = m vMomentum = 1000 kg 20/m/s/ NorthMomentum = 20,000 kg/m/s North



p = m vMomentum = 1000 kg 20/m/s/ NorthMomentum = 20,000 kg/m/s NorthMomentum = 2 x 104 kg/m/s North

• Momentum for car = 20,000 kg/m/s North

• Momentum for car = 20,000 kg/m/s North–The truck has more momentum so the

car gets pushed back.


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