Question

An object moves at a constant speed along a circular path in a horizontal XYXY.

• A. $-\left(8m/s^2\right)\hat{j}$
• B. $-\left(8m/s^2\right)\hat{i}$
• C. $-\left(4m/s^2\right)\hat{j}$
• D. $\left(4m/s^2\right)\hat{j}$

Answer 1

The correct option is A $-\left(8m/s^2\right)\hat{j}$

$P$ is the point where$x=-2m$ with velocity, $v=-4\hat{j}$

$\therefore$ radius $r=2m$

velocity $v=4m/s$

Centripetal acceleration $a_c=\frac{v^2}{r}=\frac{16}{2}=8m/s^2$

This is towards the center, therefore at

$y=2m\overrightarrow{a_c}=-\left(8m/s^2\right)\hat{j}$