Time

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What is time?

Speed & �Velocity

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What is Time?

Time is so fundamental to our existence that it’s not something we can define. However, we can still compare and measure time.

We can compare time from being longer or shorter than something. We can measure how long something takes to happen.

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Conceptual Example #7: Speed

We all know when something is fast or slow, but let’s try to describe what it means if something is fast or slow. When explaining don’t use words that synonymous to fast or slow.

Hint: Use words like distance and time to write your explanations

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Explain fast

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Explain slow

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4

When something covers a large distance in a short amount of time.

When something covers a short distance in a large amount of time.

Speed

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Math Example #5: Speed

A car is said to be able to travel 400 meters in 17 seconds. �What is the speed of this car in meters per second?

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23.53 m/s

Math Example #6: Speed

A cross country runner is running a 5 km race. It takes the cross country runner half an hour to complete the race.

1. What was the average speed of the runner in km/hr?
2. What was the average speed of the runner in km/min?

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10 km/hr

0.17 km/min

Interactive Example #1: Speed

Who here runs track? Share what your favorite running event is and what your personal record is for that event. 

Find the persons speed given the distance that person travels, and the time it takes that person.

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Conceptual Example #8: Speed

If someone is moving at a constant speed of 10 m/s, �this means that the person:

1. Increases her speed by 10m every second
2. Decreases her speed by 10m every second
3. Moves with an acceleration of 10 m/s every second
4. Moves 10m every second

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Conceptual Example #9: Speed

Which set of combinations would allow for an object to be traveling quickest, from the options that are presented. �An object travels:

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A) A “long distance” in a “long amount of time.”

B) A “short distance” in a “short amount of time.”

C) A “short distance” in a “long amount of time.”

D) A “long distance” in a “short amount of time.”

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Conceptual Example #10: Speed

An object has been considered to have moved “very fast.” �However, at the same time the same object was considered �to have moved only a “short distance,” how could this be true?

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1. The object completed the distance in a “ very long amount of time.”
2. The object completed the distance in a “ very short amount of time.”
3. Both
4. Neither

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Speed vs Velocity

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Manipulating Formulas

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Speed

Distance

Time

Math Example #7: Speed and Velocity

Cindy sees and ice cream truck and charges toward it to the right. She runs 60 meters in 8.2 seconds. 

1. What is her average velocity in m/s? 
2. What is her average speed in m/s?

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7.32 m/s or 7.32 m/s right

7.32 m/s

Math Example #8: Speed and Velocity

Jim sees a spider and lets out a loud scream! �Then, he starts running away as fast as he can to the left. �He travels 20 meters in 10.2 seconds. 

1. What is his average velocity in m/s?
2. What is his average speed in m/s?

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-1.96 m/s or 1.96 m/s left

1.96 m/s

Jim does get bitten by the spider, but does not turn into Spiderman

Conceptual Example #11: Speed and Velocity

A car is moving at 50 mi/hr (miles per hour), if it continues moving at this speed for one hour, how far would it have traveled?

1. 0 miles
2. 25 miles
3. 50 miles
4. 100 miles

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Conceptual Example #12: Speed and Velocity

A car is moving at 40 mi/hr (miles per hour), if it continues moving at this speed for half an hour, how far would it have traveled?

1. 0 miles
2. 20 miles
3. 40 miles
4. 80 miles

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Conceptual Example #13: Speed and Velocity

A car is moving at 50 mi/hr (miles per hour), if it continues moving at this speed for five hours, how far would it have traveled?

1. 0 miles
2. 10 miles
3. 50 miles
4. 250 miles

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Tips For Solving Word Problems

1. Underline key information in the question.
2. Draw out the problem, for a visual.
3. List your known variables in the question.
4. Find the unknown variable you are looking for.
5. Select a formula that has the known and unknown variables.
6. Calculate the value of the unknown.

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Math Example #9: Speed and Velocity

Jim and Harry are walking to the bus stop which is 800 meters to the left of Jim’s house. It takes them 1200 seconds to arrive. As soon as they get to the bus stop, Jim realizes he forgot his lunch and runs back home, taking 600 seconds. He then rushes back, which takes him another 720 seconds.

1. What was Jim’s average velocity in m/s for the entire trip?
2. What was Jim’s average speed in m/s for the entire trip?

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-0.317 m/s or 

-0.317 m/s Left

0.95 m/s

Jim misses the bus, but Harry is still waiting at the bus stop so that they can walk to school together. 

800 m

Jim's House

Bus Stop

Math Example #10: Speed and Velocity

Cindy is running a 5k (5000 meters) loop for her first cross-country meet. Jim wants to make sure he is at the finish line when she finishes, but he also wants to get a hotdog. Cindy usually runs with a speed of 4.3 meters/second.

1. About how long does Jim have to get his hotdog?
2. What is Cindy’s average velocity when she finishes the race?
3. Explain why Cindy’s average velocity differs from her average speed when she finishes the race.

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1162.8 s or 19.38 min

0 m/s

The displacement and the distance are different, since she is not running in a straight line.

Cindy is happy to see Jim at the finish line cheering her on. However, she gets a little annoyed because he is eating his hotdog instead of getting her any water.

Math Example #11: Speed and Velocity

Jim and Harry are having a race to get to Cindy’s house. Cindy’s house is 600 meters away. Jim runs as hard as he can with a speed of 5.3 m/s and Harry jogs with a speed of 8.2 m/s. 

How long will Harry have to wait for Jim when he gets to Cindy’s house?

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40 s

When Jim finally arrives at Cindy's house, he notices Harry and Cindy happily drinking lemonade together.

Cindy never offers Jim any lemonade.

Cindy’s House

600 m

Math Example #12: Speed and Velocity

Cindy, Harry, Kiki, and Jim are participating in a 4 x 100 meter relay race. Cindy burns everyone and runs the first 100 meters with a  speed of 8.7 m/s. Harry gets the baton and runs his 100 meters in 12.8 seconds. Kiki runs her 100 meters with a speed of 7.2 m/s. Jim almost fumbles the baton pass, but is able to hold onto it. With only one person in front of him, Jim runs as fast he can and finishes the last 100 meters in 12.4 seconds.

1. Who ran the slowest on the team?
2. What was the average speed for the entire team?

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Kiki

7.91 m/s

Jim beats the person in front of him and the whole team congratulates him. �Cindy decides that Jim should be the person to keep the trophy.