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Kinematics and Velocity/Position Graphs

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Given the acceleration graph, and the velocity and position graphs, explain how one obtains the position graph from the velocity graph. The position graph at the bottom is speeding up, then slowing down, but why not back to the 0 on the x axis? Give other examples please, with details and labelled lines, and curves if speeding up or down, etc.

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Solution Preview

Acceleration is first a positive constant, and then a negative constant, which means that velocity first increases and then decreases. In this problem, the velocity finally decreases to zero and not negative, which means that this object does not have negative ...

Solution Summary

The answer is obtained through knowledge of the properties of velocity, time, position, and acceleration. By recalling that velocity is the slope of the graph of position and time, while acceleration is the slope of graph of velocity and time, one is able to obtain the reasoning behind how transforming the position graph from the velocity graph.