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What does the slope of the graph indicate about the object's motion?
The answer will depend on whether the graph is a distance time graph or a speed time graph.The slope of a distance-time graph shows that speed of the object in the direction towards or away from the point of reference (usually the origin). It indicates absolutely nothing about its speed in any other direction. So, for example, an object could be rotating around the origin at the speed of light (the fastest possible) and the distance-time graph would show it being stationary bacause its distance from the origin is not changing!The slope of the speed-time graph indicated the acceleration of the object, again with the same qualification.
What is the shape of a displacement-time graph for an object that is constantly speeding up?
If the Object is falling at a constant velocity the shape of the graph would be linear. If the object is falling at a changing velocity (Accelerating) the shape of the graph would be exponential- "J' Shape.
What is the physical property represented by the slope of a distance time graph?
The velocity. To convince yourself, consider the units of the slope. Slope = rise/run = vertical/horizontal= distance/time=units of velocity. Alternately, consider the meaning of the graph. Where the slope is high, the distance is changing fast over a small time - high velocity.
If you decide that the duration of an instant on a position time graph is a finite period of time where is the object during that period?
If the instant is finite, the object is in the position indicated on the graph
What is the relationship between a v-t graph and a x-t graph?
An x-t graph shows displacement over time, and a v-t graph shows velocity over time. The combination of the two graphs can give you great detail about the motion of an object over a given period of time. For example, if an object moved 2 cm over 2 seconds on the x-t graph, that says nothing about what direction the object moved in, but if you combine that data with the v-t graph and see that over those 2 seconds the object had a positive acceleration, that means that the object was moving away from the origin of the graph.
