How can you let Initial position and initial velocity be equal to zero?

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Initial position and initial velocity can both be set to zero at time t = 0 when an object is at rest. At this moment, the object has not moved, resulting in both position and velocity being zero. As time progresses, the object's velocity and position will change due to acceleration. The initial conditions are crucial as they define the state of the object at the very start of observation. The equations governing motion apply for all time t ≥ 0, reflecting the changes from those initial conditions.
Miike012
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How can you let Initial position and initioal velocity be equal to zero? I understand that it will be zero at time = 0, but as time goes on from 1, 2 , 3 , 4 won't it change? I underlined that it in read in the picture?
 

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Right, well what you are looking at is at rest.

At rest, 0, the velocity is 0 because it is not moving yet. Since it hasn't moved yet, position is 0 as well. As time goes on, and the object accelerates to produce a velocity, both its velocity and position change.

Hopefully this helps.
 
when you drop something the instant it leaves what is it velocity. The position can be measure were ever you want so assign it the value of zero. Yes position and velocity will change.
 
The initial conditions are, well, the initial conditions! The time variable has value zero only once. The rock starts falling only once.

The equations provided are true for all time t \geq 0, and they can have only one set of initial conditions: whatever the state of affairs is at time t = 0.
 
thank you
 
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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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