Physics - NLM Question with Solution | TestHub

Given:
$\vec{F}=4\hat{i}-2\hat{j}+3\hat{k}$ N
$m=5$ kg
$t=10$ s
$\vec{u}=0$

Acceleration $\vec{a}=\frac{\vec{F}}{m}=\frac{4\hat{i}-2\hat{j}+3\hat{k}}{5}$

Velocity after $10$ s is given by $\vec{v}=\vec{u}+\vec{a}t$

$\vec{v}=0+\left(\frac{4\hat{i}-2\hat{j}+3\hat{k}}{5}\right)\times 10$

$\vec{v}=2(4\hat{i}-2\hat{j}+3\hat{k})=8\hat{i}-4\hat{j}+6\hat{k}$

Magnitude of velocity is $|\vec{v}|=\sqrt{8^2+(-4{)}^2+6^2}$

$|\vec{v}|=\sqrt{64+16+36}=\sqrt{116}=2\sqrt{29}$ m/s

Answer: $2\sqrt{29}$