### Requirements

• A data table
• The data table should include three columns: time, position, and time-squared. In this data table, the time and position are direct measurements, and time-squared is a calculation.
• The proper SI units should be indicated in the header of each column (seconds, meters, and seconds-squared).
• There should be at least six data points in the table, indicating six different measurements of time.
• A position-time scatter plot:
• Your graph should be on graph paper and be at least 5 inches by 5 inches.
• The scatter plot should have time labeled on the horizontal axis and position labeled on the vertical axis.
• On each axis label, the unit should be indicated.
• Each point on the data-table should be included on the scatter plot.
• The scatter plot should contain only the points. Points should not be connected, and no best fit-line or curve should be drawn.
• A brief analysis of the scatter plot:
• In only 1 -2 sentences, indicate whether the scatter plot suggests the car is accelerating.
• A linearized graph
• Your graph should be on graph paper and be at least 5 inches by 5 inches.
• The linearized graph should have position on the vertical axis and time-squared on the horizontal axis.
• The proper unit should be indicated on each of the axis labels.
• At least 6 points, corresponding to those in the data table, should be drawn.
• If the graph does not appear linear, indicate outliers, points that do not fit the general pattern, with an X and points on the line with an O.
• A hand-drawn best-ft lie should be added:
• The best-fit line should go as close to as many of the non-outlier data points (indicated by Os) as possible.
• The best-fit line should not include an arrow on the end.
• Do not take into account the outliers on the best-fit line.
• The points should be large enough that they are visible if the best-fit line goes through them.
• The best-fit line does not need to go through the origin.
• An algebraic derivation:
• By using one of the kinematic equations, determine a relationship between position and time.
• For this derivation, you can replace displacement with position in the kinematic equations. This simply indicates, without loss of generality, that the car began at the position zero.
• If any quantity is set to zero, indicate which quantity is and briefly explain why.
• Indicate if the derivation that you determine includes any constant values.
• From your derivation, indicate what quantity will be equal to the slope of the linearized graph of position vs. time-squared.
• A calculation:
• Determine the slope of your linearized graph. Do this by hand by selecting any two points on the best fit line and using the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$
• If you know how to determine slope using a linear regression, you may optionally add this piece, but also include the by hand calculation.
• Combine this slope with your algebraic derivation from above to determine a numerical value for the acceleration of the car.
• A brief analysis of the linearized graph:
• In 1-2 sentences, comment on whether the linearized graph indicates the car is moving forward with a constant, positive acceleration.
• If there are points that are outliers on your graph, and they are not the result of gross measurement error, this must mean that the car is not consistently accelerating at the same rate. If you have such points, in 1-2 sentences comment on why you think they appear.
• In 1-2 sentences comment on whether the acceleration you determined was realistic. It should be much less than 9.8 m/s/s (because that would indicate a full drop), but the order of magnitude should be 0 or -1, and not less.
• In 1-2 sentences, comment on the advantage of the linearized graph over the scatter plot.