I have completed the data table and the graphs, but I\'m stuck on the calculatio

Question

I have completed the data table and the graphs, but I'm stuck on the calculations for the questions. Can anyone please help and explain the steps I should take? Thank you! Also the `y is being used in place of a y with a line over it to indicate the mean of y.

The data table located in the Lab Report Assistant shows data taken in a free-fall experiment. Measurements were made of the distance of fall (y) at each of the four precisely measured times. From this data, perform the following operations:

Complete the table.

Plot a graph `y versus t (plot t on the x-axis or abscissa).

Plot a graph `y versus t2 (plot t2 on the x-axis). The equation of motion for an object in free fall starting from rest is y = 1?2 gt2, where g is the acceleration due to gravity. This is the equation of a parabola, which has the general form y = ax2.

Determine the slope of the line and compute an experimental value of g from the slope value. Remember, the slope of this graph represents 1?2 g. (The equations I got from the spreadsheet by doing a polynomial trendline. For y vs t - y=4.9838x^2 - 0.041x. For y vs t^2 - y=0.1164x^2 + 4.7937x)

Compute the percent error of the experimental value of g determined from the graph in step 4. (Accepted value of g = 9.8 m/s2).

Use a spreadsheet to perform the calucalations and plot the graphs indicated.

Time, t (s) Dist. y (m) Dist. y (m) Dist. y (m) Dist. y (m) Dist. y (m) `y ? t^2 0 0 0 0 0 0 -   0 0 0.5 1 1.4 1.1 1.4 1.5 1.28 0.177012241 0.25 0.75 2.6 3.2 2.8 2.5 3.1 2.84 0.248997992 0.5625 1 4.8 4.4 5.1 4.7 4.8 4.76 0.224499443 1 1.25 8.2 7.9 7.5 8.1 7.4 7.82 0.318747549 1.5625

Explanation / Answer

you have already completed the table that is great.

2) so now to plot graph Y vs t, take a graph paper and start plotting with the data you have for time data it is the first column, Y is in second column,

I think you need to plot Y vs t for other values aswel, which are there in the 3rd, 4th and 5th, 6th column

3) now as you have already calculated y' which is 1/2 * g t ^2 in column 7th, use those value with first column (time) to plot the graph between y' vs t

the graph will look like a parabola

4) slope of the graph at any point is the derivative of the equation y = 1/2 g *t^2,

take any two points in your graph and do this calculation for slope (y2 - y1)/ (t2 - t1)

5) after getting the value of g, subtract it from 9.8 to get the error, so let say you got 9.7 then error will be 9.8 - 9.7 = 0.1 and to calculate percent error

(error/ 9.8 ) *100

any doubt do ask

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