How can I improve my related rates investigation about roller skates down a hill?

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Answer :

I am taking MAA HL syllabus and I'm trying to do a calculus IA on the roller skates and my draft is due in a few days. I am modelling rates of change of roller skate accelerating down a hill, kind of like motion down an inclined plane we learn in Physics. I started off by collecting data of distance and time to generate an equation of motion of the roller skate. That gave me what I assumed is an exponential function because the roller is accelerating down the hill. To further my investigation, I tried differentiation, hoping that it would be complicated. My aim is to suggest a modification to the hill so that I would be able to travel down faster without posing any safety hazards.I'm afraid that this may too simple of an investigation for a HL syllabus. If anyone can suggest any way to sal

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