|Abstract||1. A particle moves back and forth along a line, increasing in speed. Graph. 2. How many equivalence classes in Galilean spacetime are there for a particle that is at rest? A particle that is moving at a constant speed? Why are the previous two questions trick questions? 3. In Galilean spacetime, there is no such thing as absolute velocity. Is there such a thing as absolute acceleration? If not, why not? If so, describe a spacetime in which there is no notion of absolute acceleration. Hint: to move from Aristotelian spacetime to Galilean spacetime, we got rid of the notion of absolute velocity by counting two graphs as equivalent (picturing the same spacetime) if they differed by a shear transformation. Perhaps we can get rid of absolute acceleration with an analogous move? 4. Draw a two-dimensional Cartesian grid. Label the axes x and t, and mark a scale on these axes. Make the x axis the horizontal axis, and the t axis the vertical one. Pick two points that are not on the same vertical line. Name them Ann and Bob. Label each point with its x and t coordinates.|
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