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Windup TrucksDoes the pull-back truck exhibit constant acceleration?ObjectivesDetermine if the windup truck exhibit constant accelerationCollect data using video analysisStraighten a curve to analyze direct relationships between variablesVideoThe following video shows Dr. Jones releasing his pull-back truck. Take a look at the video.Is the truck accelerating?If so, what is the direction of the acceleration?Yes the truck is accelerating in the positive direction because the velocity is getting greater as time goes on.We can tell that the truck is accelerating to the left because the velocity is getting more to the left as time goes on. It is a good idea to define left as the positive direction due to the trucks entire motion being to the left, so we can also say that the acceleration is in the positive direction.The goal of this lab is to determine if the acceleration of the truck is constant.When an object has a constant acceleration its position is directly proportional to the amount of time it’s been moving squared.To say this mathematically: x ? t2 The ? symbol means “is directly proportional to”. Pause for UnderstandingIn math class, what kind of shape is made on a y vs. x graph when y ? x2 ?ParabolaIn math class, what kind of shape is made on a y vs. x graph when y ? x ?LineIn math class, what kind of shape is made on a y vs. x graph when y = 3 ?Horizontal line, all y values are at 3In math class, what kind of shape is made on a y vs. x2 graph when y ? x2 ? LineIf a certain car had motion where x ? t2, how could you describe the motion of the car in words?The car would accelerate negatively and take more and more time to reach the next position (x)If a certain car had motion where x ? t, how could you describe the motion of the car in words?The velocity would be constant so as time goes on, the position will steadily increaseIf a certain car had motion where x = 3, how could you describe the motion in words?there would be motion and the car would remain at x=3 at time goes onDataUse the video to collect data for the position of the truck as a function of time.The orange and white lines on the sticks represent 10 cm.When the video is paused the period key advances one frame and the comma key goes back one frame.Take note of the time that the truck starts moving. Make this time t = 0s. Adjust all other times that you record to reflect this change.Time, t(s) Position, x(m)000.090.050.370.120.540.300.640.400.780.580.900.701.020.801.221.21.441.61.642.01.982.3AnalysisYou’ll be making two graphs to determine if x is directly proportional to t2.To make the first graph, plot x vs. t from the data above.When your graph is made, take a look at the different trendline options you have to best represent your data.Record the R^2 values for the different trendline options in the table below.The closer the R2 value is to 1, the better the trendline fits the data.R2 values for Different Trendlines: x vs. t graphLinear ExponentialPolynomial Order 2 Polynomial Order 3 Logarithmic0.9550.9160.9860.9960.911Which trendline fits your data the best?Polynomial Order 2What is the equation for this trendline?x = 0.366t2 + 0.546t - 0.0564Explain how your trendline shows that the truck had constant acceleration.The graph is comparing position and time. So the slope of the graph at any given point represents the velocity at that point. By looking at the graph, we can see that the slope of the line gets steeper and steeper as time progresses, constantly getting larger. Acceleration would be represented by the slope of this velocity vs time graph, and because the velocity is constantly increasing, this graph would be linear. A slope of a linear graph always remains the same, so the acceleration of the truck would be the same throughout the trial, and therefore, constantFor the second graph, plot x vs. t2.We already know that the truck has constant acceleration, but this graph will make it very clear that x ? t2 .Fill in the values for t2 in the table below and watch the following video about filling formulas in Google Sheets to save some time. Time, t2(s2) Position, x(m)000.00810.050.13690.120.29160.300.40960.400.60840.580.810.701.04040.801.48841.22.07361.6Paste a graph of x vs. t2 in the space below.Include a trendline that best fits your data.Explain how your trendline shows that the truck had constant acceleration.The Slope of the trendline represents the acceleration (M/s/s). The trend line is linear, which means that the slope stayed about the same for the whole duration of the experiment. Because the slope stayed constant, and the slope represents acceleration, the acceleration stayed constant throughout the experiment.
