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The motion of an object is depicted by a position-time graph. Various time intervals during the motion are depicted by a letter. During which time interval is the object moving and moving with the smallest constant speed?
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Position-Time Graphs:
Position versus time graphs represent changes that 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.
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The slope of the line on a position-time graph reveals information about an object's velocity. The slope is the velocity; so "as the slope goes, so goes the velocity." If the slope is 0 (as for a horizontal line), then the velocity is 0. If the slope is large, then the velocity is large. If the slope is small, then the velocity is small. If the slope is constant (as for a straight line), then the velocity is constant. If the slope is changing (as for a curved line), then the velocity is changing. If the slope is positive (sloping upward), then the velocity is positive. If the slope is negative (sloping downward), then the velocity is negative. As the slope goes, so goes the velocity.
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First, you are looking for a time interval during which the object is moving. This rules out any horizontal lines which are characteristic of objects at rest. Next you are looking for an object which has a constant speed. This rules out any curved sections which are characteristic of objects which are changing their speed. So you are looking for a time interval during which the line is NOT horizontal and NOT curved but has the smallest speed. The smallest speed would correspond to the section of the graph with the smallest slope. So eyeball each section that meets these criteria to identify the section which slopes the least (either upward or downward).
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