Initial position of an object at rest is given by 3 hat{i}-8 hat{j} It moves with constant accelerat

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3-2.Motion in Plane

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

A

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

B

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

C

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

D

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

Solution

(a)

initial position $\quad x_i=3 \quad y_i=-8$

final position $\quad x_t=2 \quad y_f=4$

$x_f-x_i=\frac{1}{2} a_x t^2=-1$

$y_f-y_i=\frac{1}{2} a_y t^2=12$

$a_x=-\frac{2}{16}=-\frac{1}{8}$

$a y=\frac{24}{16}=\frac{3}{2}$

$a=-\frac{1}{8} \hat{\imath}+\frac{3}{2} \hat{\jmath}=\text { option (A) }$

Standard 11

Physics

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