

TwoPart Kinematics Problem: Starting from rest
Martha accelerates her motor cycle forward at 5 m/s^{2} for ten
seconds then accelerates backwards at 2 m/s^{2} for ten seconds. How
fast is she going at the end of the 20 second time span described above? How
far has she traveled? Sketch the a vs.t, v
vs. t, x vs. t graphs.


Solution Define forward as positive. While the acceleration is not constant for the entire 20 seconds, clearly, it is constant during the first 10 seconds with one value and during the second 10 seconds with another value. The a vs.t, v vs. t, x vs. t are as shown at bottom right.


Conclusion and Significance When splitting a problem into multiple parts, the end conditions of the previous part become the initial conditions of the current part. Metacognition Questions: Is the acceleration constant in different parts of the problem? With constant acceleration there are essentially just two equations that can be written:
These equations are only valid for constant acceleration, but sometimes a problem can be split into separate parts in which the acceleration is constant. 
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