Average acceleration given three velocity vectors?

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The discussion revolves around understanding average acceleration given three velocity vectors. The time ordering of the vectors is crucial, as indicated by the notation t1 < t2 < t3, ensuring the correct sequence of velocities. There was initial confusion regarding whether the vectors represented time intervals, which was clarified. The importance of maintaining the correct order for accurate calculations of average acceleration is emphasized. Overall, the conversation highlights the significance of time sequencing in physics problems involving velocity.
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Can someone explain this? http://puu.sh/4LNE6.png

What is the relevance of t1 < t2 < t3
 
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t1<t2<t3 just makes sure your time-ordering is right, so you first have v1, afterwards v2, and then v3, and not some other order.
 
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Oh I was thinking of them each representing time intervals for some reason, I get it. Thanks
 
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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