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# Physics/Question pertaining to a position vs time graph

Question

acceleration vs time
What is the position of the motorcyclist at t = 40 s? What is the distance traveled by the motorcyclist in the first 40 s?

Velocity-Time Graph
the easiest way to answer this question is to convert the acceleration-time graph into a velocity-time graph. Once you have the velocity-time graph you can determine the displacement by calculating the areas under the graph! When determining the displacement any area below the x-axis is negative while any area above the x-axis is positive. For purposes of distance all of the areas are treated as being positive since distance, unlike displacement, is a scalar quantity.
Step one: Calculate the velocities at all applicable inflection points by determining the corresponding areas under the acceleration-time graph (A)
Step two: Plot the velocity-time graph.
Step three: Calculate the areas under the graph (B)
Step four: Add up the areas to determine the Displacement and Distance (C)
See attached image for the details!

Physics

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#### James J. Kovalcin

##### Expertise

I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.