How to get a Fnet vs. time graph from a velocity vs time graph.

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To derive a Fnet vs. time graph from a velocity vs. time graph, first determine the acceleration using the slope of the velocity graph. Once the acceleration is established, multiply it by the mass of the object to find the net force. The resulting Fnet vs. time graph will reflect the net force acting on the object over time. The y-axis of this graph represents the net force calculated using the formula F=ma. This method effectively connects the concepts of velocity, acceleration, and net force in physics.
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How do you find a Fnet vs time graph from either a position vs time graph, Velocity vs time, or Acceleration vs time. I know how to find Velocity vs time to position and vice versa. since the slope of the position graph tells you the velocity. I can find a acceleration from Velocity. Since slope of velocity gives you acceleration. But how do you do this find a Fnet vs. time graph from Velocity vs Time. What would the varaible even be on the y axis.

Please help.
 
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Assuming that the acceleration you have in your Acceleration vs Time graph is the net acceleration, just multiply the acceleration by the mass of whatever it is you are studying to get a Net Force vs Time graph. F=ma ;).
 
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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