Question

If position vector of a point varies with time $"t"$ as $\overrightarrow{r}=(t+t^2)(\hat{i}+\hat{j})$ meter then velocity at time $t=4s$ will be`

• A. $(6\hat{i}+6\hat{j})m/s$
• B. $(6\hat{i}+9\hat{j})m/s$
• C. $(9\hat{i}+6\hat{j})m/s$
• D. $(9\hat{i}+9\hat{j})m/s$

Answer 1

Answer: (D)

$(9\hat{i}+9\hat{j})m/s$

Given,

$\overrightarrow{r}=(t+t^2)(\hat{i}+\hat{j})m$

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

$\overrightarrow{v}=(1+2t)(\hat{i}+\hat{j})$

At $t=4sec$

$\overrightarrow{=}(1+2\times 4)(\hat{i}+\hat{j})$

$\overrightarrow{v}=(9\hat{i}+9\hat{j})m/s$

The correct option is D.