Question

A car is moving in direction $\overrightarrow{r}=-4\hat{i}+3\hat{j}$ with a speed of 10m/s. Write velocity vector of car in vector notation.

• A. $-4\hat{i}+3\hat{j}m/s$
• B. $-5\hat{i}+8\hat{j}m/s$
• C. $-8\hat{i}+6\hat{j}m/s$
• D. $-6\hat{i}+8\hat{j}m/s$

Answer 1

The correct option is C

$-8\hat{i}+6\hat{j}m/s$

Direction of motion of car is along the unit vector $\overrightarrow{r}$
$\hat{r}=\frac{4\hat{i}+3\hat{j}}{\sqrt{4^2+3^2}}=-\frac{4}{5}i+\frac{3}{5}j$
Thus velocity vector of car equal to $\overrightarrow{v}=|\overrightarrow{v}|\hat{r}$
$\overrightarrow{v}=\left(10m/s\right)(\frac{-4}{5}\overrightarrow{i}+\frac{3}{5}\hat{j})=(-8\hat{i}+6\hat{j})m/s$