Question

A force $\vec{F}=(40 \hat{i}+10 \hat{j}) N$ acts on a body of mass $5\, kg$. If the body starts from rest, its position vector $\vec{r}$ at time $t=10\, s$, will be:

• A. $(100 \hat{i}+400 \hat{j}) m$
• B. $(100 \hat{i}+100 \hat{j}) m$
• C. $(400 \hat{i}+100 \hat{j}) m$
• D. $(400 \hat{i}+400 \hat{j}) m$

Answer 1

Answer: (C)

$\frac{d \vec{v}}{d t}=\vec{a}=\frac{\vec{F}}{m}=(8 \hat{i}+2 \hat{j}) m / s ^{2}$
$\frac{d \vec{r}}{d t}=\vec{v}=(8 t \hat{i}+2 t \hat{j}) m / s$
$\vec{r}=(8 \hat{i}+2 \hat{j}) \frac{t^{2}}{2} m$
At $t=10\, \sec$
$\vec{r}=[(8 \hat{i}+2 \hat{j}) 50] m$
$\Rightarrow \vec{r}=(400 \hat{i}+100 \hat{j}) m$