suppose two different data sets were recorded after an at$-$rest billiard ball was pushed hard

while keeping all of the experimental conditions the same. The velocity was recorded as a

$6$

function of time over a fixed time interval. You will find the experimental acceleration using

both data sets provided in Table $1\mathrm{.}2.$

Time $($in s$)$ Velocity $1($in m$/$s$)$ Velocity $2($in m$/$s$)$

$000$

$31\mathrm{.}011\mathrm{.}52$

$62\mathrm{.}023\mathrm{.}03$

$93\mathrm{.}014\mathrm{.}55$

$124\mathrm{.}046\mathrm{.}06$

$155\mathrm{.}027\mathrm{.}58$

$186\mathrm{.}069\mathrm{.}09$

$217\mathrm{.}0710\mathrm{.}61$

$248\mathrm{.}0912\mathrm{.}12$

$279\mathrm{.}0813\mathrm{.}64$

$3010\mathrm{.}1315\mathrm{.}15$

Table $1\mathrm{.}2.2$ data sets for the same experimental conditions

$1.$ Type the provided data in Excel. For example, the data in the time column could be in

Column A$,$ the Velocity $1$ data could be in Column B$,$ and the Velocity $2$ data could be in

Column C$.$

$2.$ Create a $$Scatter Plot with Points$$ such that the two sets of data are visible on the same

plot. Make sure the two sets of data are represented by different symbols and colors, and

include a legend to show which data points belong to which trial.

$7$

$3.$ Add trendlines for each individual data set.

a$.$ Insert a trendline and slope equation that applies only to the first set of data

$($Velocity $1).$

b$.$ Insert a second trendline and slope equation that applies only to the second set of

data $($Velocity $2).$ Change one of the trendlines to a different color, dotted or

dashed line so that the two lines are distinguishable.

c$.$ Use some kind of labeling scheme to distinguish the two trendline equations.

d$.$ Be sure to label the axes and provide a descriptive title. Use the checklist

provided to you on page $2.$ Save this plot for your lab report.

e$.$ Record the separate slope equations in Q$1$ of In$-$Class Questions $1\mathrm{.}2.$

$4.$ Now, you want to create one data set from the two you have so that you can find a single

$$best fit$$ for all the data.

a$.$ Start by copying the two data sets into a single time column and a single velocity

column. $($You will have two columns of data instead of three.$)$

i$.$ In a new column, copy & paste the time range twice so that the time data

set is stacked on top of itself.

The new time iterations should start in a new cell right after the

previous data range ends. For example, if the first X$-$axis range is in cells

A$15-$A$25$ then the second X$-$axis range is in cells A$26-$A$36.$

ii$.$ Being consistent with the previous step, the first data set for velocity could

be copy$-$pasted into B$15-$B$25,$ and the second data set could be copypasted into B$26-$B$36.$

b$.$ Using this new data set, create a $$Scatter Plot with Points$.$ Make sure all data

points appear in the same color. Insert a trendline and show the trendline equation

on the plot.

c$.$ Be sure to label the axes and provide a descriptive title. Use the checklist

provided to you on page $2.$ Save this plot for your lab report.

d$.$ Record the separate slope equations in Q$1$ of In$-$Class Questions $1\mathrm{.}2.$

In$-$Class Questions $1\mathrm{.}2$

$1.$ What is the slope equation of the plot for

$8$

a$.$ Data Set $1$

b$.$ Data Set $2$

c$.$ Combined data sets:

$2.$ What is the slope of each plot? Remember the units.

a$.$ Data Set $1$

b$.$ Data Set $2$

c$.$ Combined data sets:

$3.$ Which billiard ball was traveling faster? How can you tell from your graph?