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

Answer 1

The correct option is A $500m$

$r\left(i\right)$=Initial position vector

$r\left(f\right)$=Final position vector

Since r is the fiction to time.

$\begin{array}{c}r\left(i\right)=r\left(0\right)=7\hat{k}\\ r\left(f\right)=r\left(0\right)=3\times {10}^2\hat{i}+4\times {\left(10\right)}^2\hat{j}+7\hat{k}\end{array}$

Now,

Displacement vector $=r\left(f\right)-r\left(i\right)$

$\begin{array}{c}D=\left|300\hat{i}+400\hat{j}+\left(7-7\right)\hat{k}\right|\\ =\sqrt{{300}^2+{400}^2}\\ =500\end{array}$

Hence, Option $A$ is correct.