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Question
position vs time
position vs time  
How can you tell simply by looking at the position-versus-time graph if there are any points of inflection?
During which time intervals is the particle slowing down or speeding up?

Answer
Inflection points are maxima or minima.  So there's an inflection point at x=0.5 and another just beyond x=2.  Any portion that's straight line means the velocity is constant.  If the curve is downward (x=0 to x=1) the particle is slowing down and going backwards.  If the curve is upward, the particle is picking up speed.  

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Richard J. Raridon

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I can answer most questions in undergraduate physics courses, including electricity and magnetism, atomic and nuclear, mechanics and optics.

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I have taught undergraduate physics courses

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Sigma Xi, AAAS, SE section of APS

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BA in math, MA in physics, PhD in physical chemistry

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