Question

A student wishes to design an experiment to show that the acceleration of an object is independent of the object's velocity. To do this, ball A is launched horizontally with some initial speed at an elevation 1.5 meters above the ground, ball B is dropped from rest 1.5 meters above the ground, and ball C is launched vertically with some initial speed at an elevation 1.5 meters above the ground. What information would the student need to collect about each ball in order to test the hypothesis?

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This is College Physics Answers with Shaun Dychko.
We have a ball launched horizontally from a table top I suppose, at 1.5 meters high, that’s ball A I think they called it. Then we have ball B which is just dropped from the table top, not given any initial velocity of any kind, so it’s just dropped. Then ball C is launched upwards into the air initially. What we want to find in each of these cases is the position of the ball at different times. So we want to create a data table of position versus time, probably seconds there and maybe meters there, for as many time intervals as possible. I suppose usually, traditionally, the independent variable is put on the left column, so time there and then the dependent variable on the right. So yeah you’re finding the position at different times, as many times as possible, the more times or the shorter the time intervals, the better for your precision. You do that for each of these balls, and then from that you can calculate what the velocities are at different times by taking the slope of the position-time graph of different times. Then from that velocity-time graph, figure out the acceleration at each of those times and then make a graph of that and then you should find that the acceleration versus time graph looks the same for each of the balls.