Physics dimensions of acceleration question

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Acceleration is defined as the change in velocity over time, expressed mathematically as a = Δv/Δt. To find the dimensions of acceleration, one must first determine the dimensions of velocity, which is length (l) divided by time (t), resulting in dimensions of LT^{-1}. Since acceleration is the change in velocity over time, its dimensions can be calculated as LT^{-1} divided by T, leading to LT^{-2}. Therefore, the dimensions of acceleration are expressed as LT^{-2}.
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i have a question from mastering physics(online site that i do my homework on) that i don't get.

Question: Find the dimensions [a] of acceleration.

Express your answer as powers of length (l), mass (m), and time (t).

and here's a small hint they give you for the equation for acceleration:

In physics, acceleration a is defined as the change in velocity in a certain time. This is shown by the a = \triangle v/\triangle t.. The \triangle is a symbol that means "the change in."

[a] = _______ (answer can only be expressed in l,m and/or t)
 
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the change in v has same demension of v... same rule applied to t,too
 
vincentchan said:
the change in v has same demension of v... same rule applied to t,too


yea, but the answer can only be in length (l), mass (m), and time (t).
 
what is the demension of v, then
 
got the answer, it's LT^{-2}
 
yup......
 
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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