Kinematics 2D: Find Particle's Accel. Vector

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SUMMARY

The discussion focuses on calculating the acceleration vector of a particle moving in the xy plane with constant acceleration. Given the initial position \(\vec{r_0} = 2\hat{i} + 4\hat{j}\) m at \(t=0\) s and the position \(\vec{r} = 8\hat{i} - 2\hat{j}\) m at \(t=3\) s, the velocity at that time is \(\vec{v} = 5\hat{i} - 5\hat{j}\) m/s. The correct method to find the acceleration vector \(\vec{a}\) involves using the formula \(\vec{a} = \frac{\Delta \vec{v}}{\Delta t}\), leading to the conclusion that the acceleration vector is \(\vec{a} = \frac{(8\hat{i} - 2\hat{j}) - (2\hat{i} + 4\hat{j})}{3}\).

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Homework Statement


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

What is the particle's acceleration vector a?

Homework Equations


The Attempt at a Solution



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

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

Could someone tell me why?
 
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