Finding X components for instantaneous velocity with points on a graph

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To find the x components of instantaneous velocity at points A-G on the graph, one must analyze the slope of the position-time graph. The instantaneous velocity is determined by the derivative of the position function, which corresponds to the slope at each point. Points C and G have zero velocity because the slope of the graph at these points is horizontal. Understanding how to derive the magnitude of velocity from the graph and then extracting the x-component is essential for solving the problem. Mastering these concepts will enable accurate calculations for all specified points.
NEAnderson90
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A test car travels in a straight line along the axis. The graph in the figure shows the car's position as a function of time. (attached figure)
Find the x component of instantaneous velocity at points A-G.

Could someone please tell me how I'm supposed to go about this problem? I know C and G are zero, but I don't know why.
 

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Hi, welcome to PF.Let me check what you already know:

- So how do you determine the magnitude of the velocity from a time-distance graph?
- How do you get the x-component from the magnitude of the velocity in this case?

If you can answer both these questions you should be able to do the question, unless there are any surprises on the (as yet invisible) image.
 
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The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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