thomasc93
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Hi, I'm a senior in high school and am currently in algebra/trig based physics. We are currently doing motion in one/two dimensions. The other day, we had a test, and we were given a distance-time graph of a boy walking home. With the graph, we were supposed to say if his velocity was constant or if he was accelerating/decelerating. The graph was a simple line (when I did a regression of various points, the calculator gave me s(t)=t/2), and I figured I could best explain this by taking the derivative of the function, since that would yield an acceleration function. Unfortunately, we were not given the velocity function, so I plugged in points from the graph and, as I said earlier, performed a linear regression, which yielded s(t) = t/2. By taking the derivative of this, I got v(t) = s'(t) = 1/2. I stated on my test that because the derivative of the velocity function was a constant, he was moving with a constant velocity (across the interval given) and therefore was not accelerating. I suppose I could have said a(t) = v'(t) = s''(t) = 0, hence giving an acceleration 0 m/s^2, but I didn't think about taking the second derivative of the distance function.
I suppose what I am asking here is the following two questions:
If I have a s/t graph and no s(t) function, is it actually valid to do a regression if I know points on the graph? Or would I just have to take a Riemann Sum?
and
Would saying that "when I took the second derivative of the distance function, it yielded 0 m/s^2" be a valid answer in an Algebra based physics class?
Thanks for your help!
I suppose what I am asking here is the following two questions:
If I have a s/t graph and no s(t) function, is it actually valid to do a regression if I know points on the graph? Or would I just have to take a Riemann Sum?
and
Would saying that "when I took the second derivative of the distance function, it yielded 0 m/s^2" be a valid answer in an Algebra based physics class?
Thanks for your help!