Kinematics 2D: Find Particle's Accel. Vector

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To find the particle's acceleration vector, the initial and final positions along with the time interval are used. The particle's initial position is at \vec{r} = 2\hat{i} + 4\hat{j} m and its position at t=3s is \vec{r} = 8\hat{i} - 2\hat{j} m. The change in position over the time interval yields a velocity of \vec{v} = 5\hat{i} - 5\hat{j} m/s. To calculate the acceleration, the change in velocity must be divided by the time interval, leading to the correct acceleration vector. The confusion arises from the incorrect application of the formula, emphasizing the need to correctly account for both the change in position and velocity.
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Homework Statement


A particle moves in the xy plane with constant acceleration. The particle is located at \vec{r} = 2\hat{i} + 4\hat{j} m at t=0s. At t=3s it is at \vec{r} = 8\hat{i} - 2\hat{j} m and has a velocity \vec{r} = 5\hat{i} - 5\hat{j} m/s

What is the particle's acceleration vector a?

Homework Equations


The Attempt at a Solution



Here's what I did
\vec{a} = (\hat{r_{1}} - \hat{r_{2}}) / \Delta t - \vec{r} = 5\hat{i} - 5\hat{j}

The answer is just that without the \vec{r} = 5\hat{i} - 5\hat{j}

Could someone tell me why?
 
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wait what is the answer?
 
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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