Question

The position vector of a particle is determined by the expression
$\overrightarrow{r}=3t^2\hat{i}+4t^2\hat{j}+7\hat{k}$. 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

$\overrightarrow{r}=3t^2\hat{i}+4t^2\hat{j}+7\hat{k}$
at $t=0,\overrightarrow{r_1}=7\hat{k}$
at $t=10sec,\overrightarrow{r_2}=300\hat{i}+400\hat{j}+7\hat{k},$
$\overrightarrow{\Delta r}={\overrightarrow{r}}_2-{\overrightarrow{r}}_1=300\hat{i}+400\hat{j}$
$|\overrightarrow{\Delta r}|=|{\overrightarrow{r}}_2-{\overrightarrow{r}}_1|=\sqrt{(300{)}^2+(400{)}^2}=500m$.