Lesson 14
Position, Speed, Direction
Let's use signed numbers to represent movement.
Problem 1
- How could you distinguish between traveling west at 5 miles per hour and traveling east at 5 miles per hour without using the words “east” and “west”?
- Four people are cycling. They each start at the same point. (0 represents their starting point.) Plot their finish points after five seconds of cycling on a number line
- Lin cycles at 5 meters per second
- Diego cycles at -4 meters per second
- Elena cycles at 3 meters per second
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Noah cycles at -6 meters per second
Problem 2
A weather station on the top of a mountain reports that the temperature is currently \(0^\circ\text{C}\) and has been falling at a constant rate of \(3^\circ\text{C}\) per hour. If it continues to fall at this rate, find each indicated temperature. Explain or show your reasoning.
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What will the temperature be in 2 hours?
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What will the temperature be in 5 hours?
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What will the temperature be in half an hour?
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What was the temperature 1 hour ago?
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What was the temperature 3 hours ago?
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What was the temperature 4.5 hours ago?
Problem 3
Fill in the missing numbers in these equations
- \(\text-2 \boldcdot (\text-4.5) = {?}\)
- \((\text-8.7) \boldcdot (\text-10) = {?}\)
- \((\text-7) \boldcdot {?} = 14\)
- \({?} \boldcdot (\text-10) = 90\)
Problem 4
- Here are the vertices of rectangle \(FROG\): \((\text-2,5), (\text-2,1), (6,5), (6,1)\).
Find the perimeter of this rectangle. If you get stuck, try plotting the points on a coordinate plane. - Find the area of the rectangle \(FROG\).
- Here are the coordinates of rectangle \(PLAY\): \((\text-11, 20), (\text-11, \text-3), (\text-1, 20), (\text-1, \text-3)\). Find the perimeter and area of this rectangle. See if you can figure out its side lengths without plotting the points.
Problem 5
Tyler orders a meal that costs $15.
- If the tax rate is 6.6%, how much will the sales tax be on Tyler’s meal?
- Tyler also wants to leave a tip for the server. How much do you think he should pay in all? Explain your reasoning.