Mission KG4 Slope Calc'ns for Position-Time Graphs

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Determine the slope (in m/s) of the line on the graph.

Include a numerical answer (no units) accurate to the second decimal place. If negative, include the - sign.

Position-Time Graphs:
Position versus time graphs represent changes which occur in an object's position with respect to time. The slope of the line is the velocity (change in position divided by the change in time) of the object.

The velocity of an object is the slope of the line (see Know the Law). The slope of a line can be determined from knowledge of two coordinate points on the line (see Math Magic section). This question asks you to determine the velocity at a stated time. Many students are tempted to simply calculated the ratio of the y to x coordinate for the point at the stated time. But don't be fooled! The slope is not the ratio y/x, it is the ratio Δy/Δx. Two coordinate points must be known and the change of each coordinate calculated. So determine what part of the graph the stated time lies upon. Then find two x-y coordinate points for that part of the graph.

The task of determining the slope of the line on a graph involves:

Pick two points on the line and determine their x-y coordinates. It is critical to select points whose coordinates are clearly known and not simply guessed at.
Based on the coordinates of these two points, determine the amount of rise of the line between the two points. The rise is the change in the y-coordinate for the line as it stretches from the first selected point to the last point.
Determine the amount of run of the line between the two points. The run is the change in the x-coordinate for the line as it stretches from the first selected point to the last point.
Calculate the ratio of rise to run: slope rise/run.
Check the sign on your slope value to insure its accuracy. A downward sloping line has a negative slope.

The Minds On Physics program calculates answers accurate to the fourth decimal place. Your answer does not need to be that accurate. The program will allow you to have a deviation of approximately 0.05 from the right answer without being wrong. This means you should enter your answer to at least the second decimal place.