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Create an experiment that relates to curvilinear motion

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I need help with a simple experiment.

I'm trying to create an experiment that relates to curvilinear motion. However, I'm unsure how to set up an experiment and show all the calculations. Can someone help me with creating a simple experiment to show what curvilinear motion is and do those calculations I can make up the data. I simply need the formulas. I was thinking about doing an experiment with a pendulum. Any suggestions will be appreciated.

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The expert creates an experiment that relates to curvilinear motion.

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The formulas that you need to consider are:
Displacement vector during time is defined by the vector :

Where ro is the initial position and r is the final position
Average velocity vector during time

Where v is the velocity vector and delta r and delta t, are the change in position and time respectively.
Instantaneous velocity vector

Average speed during time

Instantaneous speed

Total instantaneous acceleration vector

Relation between acceleration and velocity vectors

Kinematics equation for ...

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