How can you determine instantaneous velocity from a position-time graph?

chiwen1
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How would you find the instantaneous velocity if only given a position-time graph?
 
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Welcome to PF chiwen1!

The definition of instantaneous velocity is the derivative of position with respect to time:

v = dx/dt

So, on a position-time graph, this corresponds to the slope of the curve at any point.
 
BTW, if that isn't obvious then you will have to make a secant line approx.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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