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15
×
Of which equation did we derive the Height vs Time equation?
Equation of a circle (x - h)² + (y - k)² = r²
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thief
Give points!
5
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15
20
25
×
shark
Other team loses 15 points!
Okay!
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gift
Win 25 points!
Okay!
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banana
Go to last place!
Oops!
15
×
In our first step, why did we have two functions? (+/-)
To isolate for y, we needed to square root the equation, which gave a +/- value.
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15
×
At which point of the loop does the car have the most kinetic energy?
At the bottom of the loop.
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15
×
Why do we use calculus (derivatives) in this project?
To find how fast the car’s height is changing (velocity) and how that speed is changing (acceleration), which are key to understanding the motion.
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15
×
When does the first derivative of your position-time equation equal 0?
At the top of the loop.
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thief
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5
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25
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fairy
Take points!
5
10
15
20
25
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shark
Other team loses 25 points!
Okay!
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lifesaver
Give 10 points!
Oops!
15
×
If the position function is a semicircle, what general shape will the velocity graph be?
Cubic (s shape)
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heart
Other team wins 10 points!
Oops!
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rocket
Go to first place!
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fairy
Take points!
5
10
15
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25
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baam
Lose 20 points!
Oops!
15
×
What does the first derivative of a position-time graph represent?
Velocity
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15
×
Bonus: What keeps the car from falling down during the loop?
Centripetal Force
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15
×
How would the graph change if the radius of the loop doubled?
The position graph becomes wider and taller; derivatives change accordingly
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