Deriving Velocity from Distance-Time Graph: Validity and Applications

[thomasc93]

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!

 

[tatiana]

HEY, what you did thus far with taking teh derivative of the velocity fuction is correct in that you need aa second equation inorder to plug numbers into get points to produce an acceleration graph however if your in a class that is more concerned with teh mathematics of it you may only need to use the Reidman Sum in order to answer teh question being asked, without all the added steps?