Question

Position vector of a particle moving in space is given by $\overrightarrow{r}=3sint\hat{i}+3cost\hat{j}+4t\hat{k}$. Distance travelled by the particle in 2s is:

• A. 5m
• B. 10m
• C. 20 m
• D. 50 m

Answer 1

The correct option is B 10m

Given,

Position vector, $\overrightarrow{r}=3sint\hat{i}+3cost\hat{j}+4t\hat{k}$

$t=2s$

Velocity, $\overrightarrow{v}=\frac{d\overrightarrow{r}}{dt}$

$\overrightarrow{v}=3cost\hat{i}-3sint\hat{j}+4\hat{k}$

$v=|\overrightarrow{v}|=\sqrt{(3cost{)}^2+(-3sint{)}^2+(4{)}^2}$

$v=\sqrt{9(co{s}^{2}t+si{n}^{2}t)+16}=\sqrt{9+16}$

$v=5m/s$

Distance travelled by the particle in $2s$ is

$d=vt$

$d=5\times 2=10m$

The correct option is B.