Question

The position vector of a particle is determined by the expression $\overline{r}$ = 3 $t^2$ $\hat{i}$ + 4 $t^2$$\hat{j}$ + 7$\hat{k}$ .The distance traversed in first 10 sec is

• A. 500 m
• B. 300 m
• C. 150 m
• D. 100 m

Answer 1

The correct option is A 500 m

As the particle moves in a straight path, the magnitude of displacement is equal to the distance travelled by the particle
$\overrightarrow{r}$ = 3 $t^2$ $\hat{i}$ + 4 $t^2$$\hat{j}$ + 7$\hat{k}$
at t = 0, $\overrightarrow{r_1}$ = 7$\overline{k}$
at t = 10 sec,$\overrightarrow{r_2}$ = 300 $\hat{i}$ + 400$\hat{j}$ + 7 $\hat{k}$
$\overrightarrow{△}r$ = ${\overrightarrow{r}}_2$ - ${\overrightarrow{r}}_1$ = 300$\hat{i}$ + 400$\hat{j}$
|$\overrightarrow{△}r$| = | $\overrightarrow{r_2}$ - $\overrightarrow{r_1}$| = $\sqrt{{\left(300\right)}^2+{\left(400\right)}^2}$ = 500m