Graphical Analysis of Motion

In lab 1.7, the displacement and acceleration of a moving body was obtained by using a "Velocity v. Time" graph. The hypothesis was, "The displacement and acceleration of the cart can be obtained by making a graph using information from a cart, a track, a weight and photogates." At first, the pulse mode of the photogates was used to determine how time would affect displacement. The data was then put into a graph labeled "Displacement vs. Time". The second part of the lab was to determine how instantaneous velocity would be affected by time by using the gate mode in the photogates. This data was then put into graph labeled "Velocity vs. Time". The third and final part of the lab was to calculate the slopes of each graph when the time was equal to 0.80 seconds and to calculate the area of the velocity graph during that time.

The first summary question asked to describe the meanings of the slopes of the graphs obtained in part III. The slope of the Displacement vs. Time graph was a representation of instantaneous velocity at 0.80 seconds into the trial. The slope the Velocity vs. Time graph was a representation of acceleration at 0.80 seconds into the trial. The second summary question asked to describe the motion of the cart based on the results from the Velocity v.Time graph. The cart's motion was influenced by time. As time increased, the cart's velocity also increased. The car was accelerating up the ramp, until the weight hit the ground, at which point the acceleration automatically turned negative due to gravity. The third summary question asked during which segments of time the cart had a certain acceleration (positive or negative). Up until the weight hit the ground, the acceleration of the cart was always positive. However, the instant the weight hit the ground, the acceleration automatically turned negative, due to the effect of gravity on the cart, slowing the cart down until it reached a velocity of zero at it's highest point, then turning the velocity negative.

To find the percent error, the equation for percent error had to be used. This equation is (accepted value - calculated value) / (accepted value) * 100. To find the percent error, the slope of the Displacement vs. Time graph at 0.8 seconds was compared to the data of the Velocity vs. Time graph at 0.8 seconds, with the Velocity vs. Time graph slope being the accepted value. The percent error calculated ended up being fill this in. We also had to compare the displacement for time = 0.8sec from the Displacement vs. Time graph to the displacement for time = 0.8sec from the Velocity vs Time graph. This percent error calculated to be fill this in. During the experiment, there were sources of error that could have changed our results from being perfect. One possible source of error for this experiment was that the photogates could not be set perfectly since the base was so wide. This would result

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