How to Convert Position Time Graphs to Velocity Time Graphs
The position of an object over time is directly related to how quickly the object is moving during that time. This direct relationship is displayed in their graphs. A mathematical definition of a quantity, called a function, can be manipulated in such a way as to give another function, called a derivative, which describes the slope of the initial function. A velocity-time graph is the derivative of its corresponding position-time graph. As such, a position-time graph can be converted to its derivative velocity-time graph by finding the slope of the position-time graph at multiple points and tracing the new velocity-time curve.
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Instructions
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Locate the left endpoint of the interval on the position-time graph that is being converted to a velocity-time graph.
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Find the slope at this end point by determining the (rise / run) between the end point and the point succeeding the end point. For example, if your graph is measured along the x-axis in unit of 1 (the run), and the y-value (the rise) at the point succeeding the end point is 4 units then the slope of that interval is: 4 / 1 = 4.
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Use the (rise / run) slope determination method for each interval until you reach the right endpoint. Write the slopes down as you go and identify each slope with the interval they describe.
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Notice that at points on the position-time graph where the graph is horizontal, the slope equals zero. Mark these points on the velocity-time graph as x-intercepts.
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Mark the velocity-time graph using the slopes of the position-time graph as the y-values at the corresponding x-values of the position-time graph.
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Connect the points together with a smooth, curved line, from endpoint to endpoint.
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