Precision is measured based off of how small of a definite measure a person can measure. The smaller the discrepancy, the more precise a measurement is. The smaller the amount that is $pm$ the more precise the measurement.

$$
dfrac{1m}{100cm}; dfrac{1,000m}{1km}
$$

$$
86.2cm cdotdfrac{1m}{100cm}
$$

$$
.862m cdot dfrac{1km}{1,000m}
$$

$$
8.62 times 10^{-4} km
$$

$slope=dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$
where $(x_{2},y_{2})$ and $(x_{1},y_{1})$ are points on lying on the line.

Mark 2 points on the straight line and name them $(x_{1},y_{1})$ and $(x_{2},y_{2})$. The points are chosen such that the x-axis and y-axis numbers for both the points turns out to be integers. This will help us in solving when we replace these values in the formula for obtaining slope.

$(x_{1},y_{1}) = (0 m/s, 0 s)$

$(x_{2},y_{2}) = (8 m/s, 2 s)$

$slope=dfrac{(2-0)m/s}{(8-0)s}=dfrac{1}{4} m/s^{2}=0.25$ $m/s^{2}$

Replace the values for $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the slope formula alongwith the necessary units for quatities represented by $x$ and $y$ axis. Solve and since all our options are in decimals it is better to convert the answer from fraction to decimal with proper units.

$$
D = dfrac{m}{V}
$$

$$
dfrac{VD}{D} =dfrac{m}{D}
$$

$$
V = dfrac{m}{D}
$$

a) The equation F=ma rewritten so a is in terms of F and m is: a=$dfrac{F}{m}$

b) You will need a conversion factor of $10^{-3}$

There are 1000 grams in 1 kilogram so you need to multiply the grams by $10^{-3}$ with equals 0.001 to get the number of grams in kilograms

c) The equation you will use is: a = $dfrac{F}{m}$

The conversion factor is $10^{-3}$, multiply the grams by the conversion factor to get the kilograms:

$350times$ $10^{-3}$ = 0.35 kg

Sub the given F and the m in kg and solve of a:

a = $dfrac{2.7}{0.35}$

= $7.71 m/s^{2}$

$therefore$ the acceleration is $7.7 m/s^{2}$

a) a = $dfrac{F}{m}$
b) $10^{-3}$
c) $7.7 m/s^{2}$

$$
textbf{underline{textit{Solution}}}
$$

By plotting the points using Excel, we find that the equation of best fit line ”trend line” is given by the following equation

$$
tag{1} y= -1.03 x + 11.54
$$

$textbf{Or }$we can just draw the line by hands which best fits all the points, and then find the slope from any 2 points on the best fit line with coordinates ($x_1,y_1$) and ($x_2,y_2$) through the following equation

$$
m = dfrac{y_2 – y_1}{x_2 – x_1}
$$

And then we find the point $c$ of $y$-intercept “that is it, the point where $x=0$”, and then substituting in the general equation of the straight line, where

$$
y=mx+c
$$

$textbf{underline{textit{note:}}}$ sometimes we get a physical situation, where the plot best fit line must pass through the origin, intercept at some value in $y$-axis in this problem we are free to chose the $y$-intercept which enables us to have the fitting curve which fits all the points with the least error.

Check, the following $textbf{Graph}$ where we plotted the points in the graph and draw the best fit line whose equation is given by (1)

$$
y= -1.03 x + 11.54
$$