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**Speed, Velocity and Acceleration**

Measuring motion

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**Measuring Distance Meter – international unit for measuring distance.**

1 mm = 50 m

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**We use the variable speed to describe how quickly something moves.**

Saying a race car, runner, or plane is “fast” is not enough to accurately describe its speed scientifically.

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**The speed of a bicycle is the distance it travels divided by the time it takes.**

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**Constant means “does not change” so constant speed is speed that does not change.**

How do we know the speed of the bike is constant?

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Since speed is a ratio of distance over time, the units for speed are distance units over time units.

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**An equation can be used to calculate speed, distance, or time if two of the three values are known.**

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**S = d/t Calculating Speed**

Speed (S) = distance traveled (d) / the amount of time it took (t). S = d/t

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Units for speed Depends, but will always be a distance unit / a time unit Ex. Cars: mi./h Jets: km/h Snails: cm/s Falling objects: m/s

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**S = d/t Calculating speed**

If I travel 100 kilometers in 1 hour then I have a speed of… 100 km/h If I travel 1 meter in 1 second then I have a speed of…. 1 m/s

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**The speed found by dividing the total distance by the total time is the average speed.**

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**Average speed Speed is usually NOT CONSTANT**

Ex. Cars stop and go regularly Runners go slower uphill than downhill Average speed = total distance _________________ total time

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**Calculating Average Speed**

It took me 1 hour to go 40 km on the highway. Then it took me 2 more hours to go 20 km using the streets. Total Distance: 40 km + 20 km = 60 km Total Time: 1 h + 2 h = 3 hr Ave. Speed: total d/total t = 60 km/3 h = 20 km/h

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Question I jogged 100 m in 60 seconds. I then ran another 100 m uphill in 60 seconds. What is my average speed? A) 100 /min B) 2000 m/min C) 100 m/min D) 200 m/min E) 20 m/min Total Dist. = 100 m m = 200 m Total Time = 60 s + 60 s = 120 s = 2 min Ave speed = total dist/total time = S = 200 m / 2 min = 100 m/ min

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**How fast is a snake moving that can slither 20 meters in 5 seconds?**

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**It took Grandma 1.5 hours to drive 150 kilometers from her house to mine. How fast was she driving?**

It takes Brooke 20 minutes to run 100 meters. What is her speed in meters per minute?

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**Velocity Velocity – SPEED with DIRECTION of an object. Example:**

An airplane moving North at 500 mph A missile moving towards you at 200 m/s

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**Question What is the difference between speed and velocity?**

Speed is just distance/time. Velocity also includes direction. Speed is just distance/time. Velocity includes direction as well.

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Some practice 1. Calculate the average speed of a car that travels 280 km in 4 hours. 2. You ride your bicycle at an average speed of 15 km/h for 2 hours. How far did you go? 3. How long will it take you to run 100 meters if you run at 5 m/s?

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More Practice... If a car drives 490 miles in 6 hours, how fast did it drive? If a rocket flies 17,000 miles per hour for 12 hours, how far will it go? If an airplane flies 800 miles at 300 miles per hour, how long will it take them to get there?

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**In order to compare variables they must be in the same units.**

Comparing Variables In order to compare variables they must be in the same units. To convert between units, you multiply and/or divide by conversion factors. A conversion factor is an equivalent ratio.

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**Using conversion factors**

Conversion factors are translators between one language of units and another.

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**Velocity: Direction Matters**

Velocity is the speed of an object in a particular direction. Do not use velocity and speed in the same way because they are NOT the same thing!

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**The difference between speed and velocity is DIRECTION!**

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**Velocity will always include a direction!**

The velocity of a plane headed to California might be 600 km/h west. The velocity of a train headed to New York might be 90 km/h north.

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**Which are examples of velocity?**

m/s forward 2. 1,500 km/hr m/s south cm/s down mph

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**How to combine velocities**

If 2 velocities are going in the same direction, add them together. If 2 velocities are going in opposite directions, subtract the smaller from the larger. The resulting direction will continue to be that of the larger velocity.

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Velocity Practice A car travels with a velocity of 20 m/s to the west. An insect inside the car flies with a velocity of 2 m/s to the east. What is the resultant velocity of the insect? Don’t forget, your answer must include a direction!!

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**More Velocity Practice**

A bus is traveling forward at 30 km/h. You get up from your seat and walk toward the driver at a speed of 2 km/h. What is your resultant velocity?

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**Velocity will change if:**

1. The direction of travel changes: Example: A plane takes off to the east and then makes a turn to head north…it has changed velocity. 2. The speed of travel changes: Example: The car slows down to leave the highway to go down an exit ramp.

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**Graphing Speed: Distance vs. Time Graphs**

Denver Phoenix

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**Graphing Speed: Distance vs. Time Graphs**

Speed = Slope = Rise/Run Rise

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**Graphing Speed: Distance vs. Time Graphs**

Speed = Slope = Rise/Run Rise=? 600 km 3 hr

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**Graphing Speed: Distance vs. Time Graphs**

Speed = Slope = Rise/Run Rise=? 600 km 3 hr Rise/Run = 600 km/3 hr = 200 km/hr

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Question What does the slope of a distance vs. time graph show you about the motion of an object? It tells you the SPEED

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Question Below is a distance vs. time graph for 3 runners. Who is the fastest? Leroy is the fastest. He completed the race in 3 hours

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**Acceleration Acceleration = speeding up**

Acceleration – the rate at which velocity changes Can be an: Increase in speed Decrease in speed Change in direction

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**Types of acceleration Increasing speed Decreasing speed**

Example: Car speeds up at green light Decreasing speed Example: Car slows down at stop light Changing Direction Example: Car takes turn (can be at constant speed) screeeeech

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Question How can a car be accelerating if its speed is a constant 65 km/h? If it is changing directions it is accelerating

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**Calculating Acceleration**

If an object is moving in a straight line Units of acceleration: m/s2

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**Calculating Acceleration**

0 s 1 s 2 s 3 s 4 s 0 m/s 4 m/s 8 m/s 12 m/s 16 m/s

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Question A skydiver accelerates from 20 m/s to 40 m/s in 2 seconds. What is the skydiver’s average acceleration?

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**Graphing Acceleration**

Can use 2 kinds of graphs Speed vs. time Distance vs. time

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**Graphing Acceleration: Speed vs. Time Graphs**

Speed is increasing with time = accelerating Line is straight = acceleration is constant

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**Graphing Acceleration: Speed vs. Time Graphs**

Rise = 4 m/s Run = 2 s In Speed vs. Time graphs: Acceleration = Rise/Run = 4 m/s ÷ 2 s = 2 m/s2

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**Graphing Acceleration: Distance vs. Time Graphs**

On Distance vs. Time graphs a curved line means the object is accelerating. Curved line also means your speed is increasing. Remember slope = speed.

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**Question Run = 3 s Rise = -6 m/s**

Above is a graph showing the speed of a car over time. 1) How is the speed of the car changing (speeding up, Slowing down, or staying the same)? 2) What is this car’s acceleration? The car is slowing down Acceleration = rise/run = -6m/s ÷3s = -2 m/s2

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**curved line = accelerating, flat line = constant speed**

Question: The black and red lines represent a objects that are accelerating. Black is going a greater distance each second, so it must be speeding up. Red is going less each second, so must be slowing down Remember: in distance vs. time graphs: curved line = accelerating, flat line = constant speed Which line represents an object that is accelerating?

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