Question

A particle $P$ starts from the origin with velocity $\overrightarrow{u}=(2\hat{i}-4\hat{j})m/s$ with constant acceleration $(3\hat{j}-5\hat{j})m/s^2$ after travelling for $2$ second its distance from the origin is

• A. $10m$
• B. $20.6m$
• C. $9.8m$
• D. $11.7m$

Answer 1

The correct option is B $20.6m$

$\overrightarrow{s}=\overrightarrow{u}t+\frac{1}{2}\overrightarrow{a}{t}^2$

$\overrightarrow{s}=(2\hat{i}-4\hat{j})2+\frac{1}{2}(3\hat{i}-5\hat{j})(2{)}^2$

$\overrightarrow{s}=(4\hat{i}-8\hat{j})+(6\hat{i}-10\hat{j})$

$\overrightarrow{s}=(10\hat{i}-18\hat{j})$

$|\overrightarrow{s}|=\sqrt{(10{)}^2+(18{)}^2}$

$|\overrightarrow{s}|=\sqrt{100+324}$

$|\overrightarrow{s}|=\sqrt{424}$m =20.6 m