The initial position of an object at rest is | vedclass

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Question

(A) Given that the object starts from rest,the initial velocity $u = 0$. The initial position is $\vec{r}_i = 3 \hat{i} - 8 \hat{j}$ and the final pos

Vedclass · Accepted Answer

$-\frac{1}{8} \hat{i}+\frac{3}{2} \hat{j}$

Vedclass · Answer

(A) Given that the object starts from rest,the initial velocity $u = 0$. The initial position is $\vec{r}_i = 3 \hat{i} - 8 \hat{j}$ and the final position is $\vec{r}_f = 2 \hat{i} + 4 \hat{j}$. The displacement $\vec{s} = \vec{r}_f - \vec{r}_i = (2 - 3) \hat{i} + (4 - (-8)) \hat{j} = -1 \hat{i} + 12 \hat{j}$. Using the equation of motion $\vec{s} = \vec{u}t + \frac{1}{2} \vec{a} t^2$,where $t = 4 \, s$ and $\vec{u} = 0$: $-1 \hat{i} + 12 \hat{j} = \frac{1}{2} \vec{a} (4)^2$. $-1 \hat{i} + 12 \hat{j} = 8 \vec{a}$. Therefore,$\vec{a} = \frac{-1 \hat{i} + 12 \hat{j}}{8} = -\frac{1}{8} \hat{i} + \frac{12}{8} \hat{j} = -\frac{1}{8} \hat{i} + \frac{3}{2} \hat{j}$. Thus,the acceleration is $-\frac{1}{8} \hat{i} + \frac{3}{2} \hat{j}$.

The initial position of an object at rest is given by $3 \hat{i}-8 \hat{j}$. It moves with constant acceleration and reaches the position $2 \hat{i}+4 \hat{j}$ after $4 \, s$. What is its acceleration?

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