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What does the first derivative of a position-time graph represent?
Velocity
If the position function is a semicircle, what general shape will the velocity graph be?
Cubic (s shape)
Bonus: What keeps the car from falling down during the loop?
Centripetal Force
Of which equation did we derive the Height vs Time equation?
Equation of a circle (x - h)² + (y - k)² = r²
How would the graph change if the radius of the loop doubled?
The position graph becomes wider and taller; derivatives change accordingly
When does the first derivative of your position-time equation equal 0?
At the top of the loop.
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.
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.
At which point of the loop does the car have the most kinetic energy?
At the bottom of the loop.
