Question

A particle has an initial velocity of ($3\hat{i}+4\hat{j}$) m/s and a constant acceleration of $(4\hat{i}-3\hat{j})m/s^2$. Its speed after one second will be equal to:

• A. 0
• B. $7\sqrt{2}\frac{m}{s}$
• C. $\sqrt{5}0\frac{m}{s}$
• D. 25 m/sec

Answer 1

Answer: (C)

$\sqrt{5}0\frac{m}{s}$

Initial velocity of particle $\overrightarrow{u}=$ $3\hat{i}+4\hat{j}$
Acceleration $\overrightarrow{a}=$ $4\hat{i}-3\hat{j}$
Final velocity after 1 second $\overrightarrow{v}=\overrightarrow{u}+\overrightarrow{a}t$
where $t=1s$
$⟹\overrightarrow{v}=$ $(3\hat{i}+4\hat{j})+$ $(4\hat{i}-3\hat{j})\times 1=$ $7\hat{i}+\hat{j}$
Speed after 1 second $|\overrightarrow{v}|=\sqrt{7^2+1}=\sqrt{50}m/s$