Calculate the terminal velocity from a displacement-time graph?

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To calculate terminal velocity from a displacement-time graph, identify the point where the graph transitions from a quadratic to a linear shape, indicating constant velocity. The gradient of this linear section represents the terminal velocity, as it reflects the maximum speed reached when acceleration is zero. Understanding that terminal velocity is constant is crucial, and it occurs when the forces acting on the object balance out. While factors like mass and drag are relevant in a broader context, they are not necessary for this specific calculation. Focus on determining the maximum gradient of the linear portion of the graph to find the terminal velocity.
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Hi

Can someone please explain how I can calculate the terminal velocity from a displacement-time graph? I'm only finding solutions to velocity-time graphs, but that's not what I need.

Thanks in advance.
 
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What is the definition of terminal velocity?
 
EDIT:removed... too much explaining
 
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I understand terminal velocity to be the velocity reached by a falling body when it experiences zero acceleration... All I have is the displacement and time to work with and I know that the gradient of the graph will give me the velocity. I'm just confused if the value I'll get for the gradient is actually the terminal velocity I'm being asked for or not. When I've looked this up, I'm seeing other things about the mass, drag, density, etc. to get the terminal velocity. Since I wasn't given these values I'm thinking the most logical thing is to find the gradient, but this may be wrong. Any help would be really appreciated here.
 
You know that terminal velocity is the maximum speed and it is constant. You know that velocity is the gradient. So why don't you try the maximum gradient that is constant.
 
While accelerating, displacement is quadratic, velocity is linear, and acceleration is constant. At terminal velocity, displacement is linear, velocity is constant, and acceleration is zero. Find the slope where the graph becomes linear
 
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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