Speed, Velocity, and Acceleration

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Speed, Velocity, and Acceleration

• An Interactive Power Point

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Speed

• To calculate speed use the equation
• Speed distance
• time
• Speed only gives distance and time

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Speed Units

• m/s
• km/s
• m/h
• km/h
• When you read the first unit, you say meters
  PER second.
• Do not write mps

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Average Speed

• On a trip from Chicago to Texas could you stay
  the same speed?
• You could get an average of all the speeds during
  the trip.

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How do we calculate average speed?

• The total distance of the trip divided by the
  total time of travel.

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Magic Triangle

• This triangle tells you the formulas you need for
  speed, distance, and time
• s d
• t
• d s x t
• t d
• s

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Speed Problems

• A baseball moves 11 m in 1 sec. What is its
  speed?
• Speed distance
• time
• A car travels 70 km in 1.75 h (hours). What is
  its speed?
• S D
• T

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Speed is Relative!

• What does it mean when we say that a car moves at
  a rate of 80 km/h?
• What do we mean that it is relative to?
• Unless the problem says something else, the
  motion that we discuss is ALWAYS relative to
  Earth.

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What is Velocity?

• Describes the motion and the direction.
• Even if speed remains the same, if the direction
  changes then the velocity has changed.

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Follow the steps to solve an equation.

• Problem You walk 5 meters in 3 seconds. What is
  your velocity?
• Step 1 Write what you know.
• d 5 meters
• t 3 seconds
• v ?
• Step 2 Write the formula you will use. v d / t
• Step 3 Put the numbers in for the variables that
  you know.
• v 5 meters
• 3 seconds
• Step 4 Do the math.
• v 1.6667meters/seconds 1.7m/s
• Your velocity is 1.7 meters per second.

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Equations for Speed and Velocity

• v d
• t
• d v ? t
• t d
• v
• You can replace the s(speed) in the triangle for
  v(velocity)

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Calculating Average Speed / Velocity

• d distance
• v speed / velocity
• t time

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Sample Speed / Velocity Problems

• A car travels a distance of 16 m in 1.8 seconds.
  What is its speed?
• d 16 m
• t 1.8 s
• v ?
• v d
• t
• v 16m
• 1.8 s
• v 8.89 m/s

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Sample Speed / Velocity Problems

• Sound travels at a speed of 330 m/s. If a
  lightning bolt strikes the ground 1 km away from
  you, how long will it take for the sound to reach
  you?
• v 330m/s
• d 1km
• t ?
• t d
• v
• t 1km
• 330m/s You must change the km to m
• t 1000m Kids Havent Died By Doing
  Crazy Metric
• 330m/s
• t 3.03 s

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Practice Problems

• 1.   Calculate the speed of a dog running through
  a field if he is covering 23.7 meters in 54
  seconds.
• 2.   If a cross country runner covers a distance
  of 347 meters in 134 seconds what is her speed?
• 3.   What is the speed of a baseball that
  travels 49 meters in 2.4 seconds?

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Practice Problems

• 4.   What is the speed of a horse in meters per
  second that runs a distance of 1.2 miles in 2.4
  minutes?  
• 5.   Calculate the velocity of a car that
  travels 556 kilometers northeast in 3.4 hours.
   Leave your answer in kilometers per hour.
• 6.   If the distance covered by a jogger is
  2,541meters through the park and the time it took
  to cover that distance was 43.6 minutes, what was
  the speed of the jogger?

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Practice Problems

• 7.   Which object has a greater velocity, a ball
  rolling down a 3.4 meter hill in six seconds or a
  fish swimming upstream and covering 5.4 meters in
  0.4 minutes?
• 8.   If Seneca decides to walk across town to a
  store that is .95 kilometers away and she has
  only 25 minutes to get there, what speed does she
  need to maintain to arrive on time?
• 9.   If a projectile flies north 387 meters in
  5.8 seconds, what is its velocity?
• 10.   Calculate the velocity of a mountain
  climber if that climber is moving northeast at a
  pace of 1.6 km in 1.4 hours?  Give your answer in
  the SI unit for velocity.

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• Acceleration

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What is Acceleration?

• The rate of change of velocity.
• Car commercial ? 0 to 60 mph in 10 seconds.
• Speeding up
• The amount of change of velocity in a time
  interval.

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Acceleration

• The rate at which velocity changes
• Acceleration is
• Increasing speed
• Decreasing speed
• Changing direction

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How do you measure a change?

• The water was at 50m and it rose to 100m. What
  is the change?
• We started at 900am and the class was over at
  1100am. What is the change?
• The dog grew from 8 lbs to 15 lbs. What is the
  change?
• We had 20 gallons, and now we have 5. What is
  the change?

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Increasing speed

• Increase in speed increase in acceleration
• Exa car moving from a stopped position

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Decreasing speed

• Decrease in speed deceleration (negative
  acceleration)
• Ex a car decelerates as it stops at a red light

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Changing direction

• Any change in direction is considered
  acceleration, even if the objects speed remains
  constant
• Ex a Ferris wheel accelerates because it moves
  in a circle (changes direction).
• Its speed is constant

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Calculating Acceleration

• Calculate the change in velocity during each unit
  of time
• Acceleration final velocity initial velocity
• final time
  initial time
• OR
• change in velocity (speed)
• time it took for change

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How to Calculate Acceleration?

• means change in

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How do you calculate ?v?

• The change in velocity the final velocity the
  initial velocity.
• ?v vf vi
• You are stopped at a red light. When it turns
  green, you speed up to 45m/s. What is your
  change in velocity?
• vi 0m/s
• vf 45m/s
• ?v ?
• ?v vf-vi 45m/s- 0m/s 45m/s

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• Velocity is measured in meters/second
• Acceleration is measured in meters per second per
  second or m/s2
• Acceleration 22 m/s 4 m/s
• 3 s
• A 18 m/s
• 3 s
• A 6 m/s/s or 6m/s2

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Lets Practice with some Problems

• A cars velocity changes from 0 m/s to 30 m/s in
  10 seconds. Calculate the cars average
  acceleration.
• Acceleration final velocity initial velocity
• change in time
• A 30 m/s 0 m/s
• 10s
• a 30 m/s
• 10s
• a 3 m/s/s or 3 m/s2

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Practice Problem

• In 2.5 s a car increases its speed from
• 60 km/h to 65 km/h while a bicycle goes from
  rest to 5 km/h.
• Which undergoes the greater acceleration?
• What is the acceleration of each vehicle?

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Answer A ending speed initial speed
time interval

• Cars acceleration
• a 65 km/h 60 km/h 5 km/h 2km/h/s
• time interval 2.5 s
• Bicycles acceleration
• A 5 km/h 0 km/h 5km/h 2 km/h/s
• 2.5 s 2.5 s

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What is negative acceleration?

• Also known as DECELERATION.
• The negative rate of change of velocity.
• Slowing down.
• The amount of negative change of velocity in a
  time interval.
• Ex
• 10m/s 25 m/s - 15 m/s - 3m/s/s or 3m/s2
• 5 s 5 s