Graphical Analysis of Motion

The concept of the lab mainly focused on kinematics. Kinematics is the branch of mechanics dealing with motion of an object without discussing force and mass. A moving body always has displacement, velocity, and acceleration. Any one of these values can be determined from a graph that involves time, displacement, and velocity. The objective of the lab was to obtain the displacement and the acceleration of a moving body from its Velocity vs. Time graph. Displacement is how far an object travels or the total path an object moves on, including its direction. Velocity is how fast an object moves and in what direction it is moving. Lastly, acceleration is how fast the velocity is changing or rate at which velocity is changing. In order to create a Velocity vs. Time graph, the instantaneous velocity was determined at different distances. Instantaneous velocity is the velocity of an object at a given instant, especially when the object is accelerating. Given just a cart, a ramp with a ruler at the edge of it, "photogates," string and a device to calculate the time, it was hypothesized that acceleration can be found by determining the slope of the Velocity-Time graph and the displacement can be found by determining the area under the line or curve of the graph.

A source of error from the experiment was that it was difficult to line up the card at the 20 centimeter mark. It could have been off by 1 millimeter or more and the starting point could have been different each trial. To resolve this situation, we can line up the cart at a certain mark to make the starting point of each trial consistent. Uneven friction was another source of error. The uneven friction caused by possible bumps on the track may result in un-uniform acceleration. Therefore, the points on the VT graph do not connect to form a straight line because at some points, the acceleration is different. This problem could be avoided if we smooth wheels were used.

The slope determined in part III for the Displacement vs. Time graph represents the instantaneous velocity of the cart at the time of 0.8 seconds. The second slope, for the Velocity versus Time graph, represents the acceleration of the cart as a result of the falling mass, essentially the change in velocity over that same amount of time. Based on the graphs obtained in Part III, it was shown that both slopes were positive. This means that as the cart increases displacement or velocity, the slope of the Displacement vs. Time graph should equal to the velocity of the object. Based on the results from the Velocity vs. Time graph, the motion of the cart was similar to the motion of a free falling object. Based on the Velocity vs. Time graph, the cart had a positive acceleration during the time from 0.0 seconds to 1.15 seconds. A positive acceleration meant that the car was accelerating or speeding up because the change in velocity over time was positive. When the velocity of the cart reached its maximum point a