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## Homework Statement

I have to construct two graphs ( distance vs time and instantaneous speed vs time) based off of a lab in which we made measurements based off of a spark timer and paper tape. I made the following measurements and constructed the D vs T graph based off of them:

t / "x" in meters

0.0 / 0.00

0.1 / 0.0360

0.2 / 0.161

0.3 / 0.382

0.4 / 0.697

0.5 / 1.109

0.6 / 1.614

My question is pertaining to making the instantaneous speed vs time graph

For this, we had to find the instantaneous speed at the midpoint of each interval.

"From your distance vs time graph, find the instantaneous speed at the midpoint of each 0.1 second interval. You can do this by either drawing a tangent line at the midpoint of each interval and determining its slope, or by finding the average speed for each of the intervals."

I was a bit confused by this instruction. Drawing a tangent line was and finding the instantaneous speed was impossible, so the teacher told us to find the average speed for each interval.

## Homework Equations

t2-t1/s2-s1 (I think)

## The Attempt at a Solution

To find the IS, I first found the midpoint of the time interval (ex: (0.2 + 0.3)/2]= 0.250. Then I divided the displacement of the interval by the midpoint of the time interval (ex: interval 0.2-0.3) (0.382-1.161)/0.250 = 0.884

Time interval /Midpoint of interval /Inst. speed in m's

0.0-0.1 / 0.0500 / 0.720

0.1-0.2 / 0.150 / 0.833

0.2-0.3 / 0.250 / 0.884

... ... ...

I feel like my calculations are incorrect. Also, when plotting the graph would the instantaneous speed be plotted against the time (ex. 0.720/ 0.1) or against the midpoint of the interval (0.0720/0.05)? I plotted form 0.720 / 0.1, and I came up with a graph that looked rose up from zero and leveled off, like a logarithm graph beginning at zero.