Question

The position of a particle is given by $\overline{r}=3t^2\hat{ı}+3t\hat{ȷ}+4\hat{k}$ where $t$ is in second and the coefficient have proper units for $\overline{r}$ to be in meter. The acceleration of the particle at $t=2s$ is

• A. $4{ms}^2\text{along}y-direction$
• B. $3{ms}^{-2}\text{along}x-direction$
• C. $4{ms}^{-2}\text{along}x-direction$
• D. $2{ms}^{-2}\text{along}z-direction$

Answer 1

The correct option is A $4{ms}^2\text{along}y-direction$

Given,

$\overline{r}=2t^2\hat{i}+2t\hat{j}+4\hat{k}$

Now,

Velocity will be

$\begin{array}{c}V=\frac{dr}{dt}=3\hat{i}+8\hat{j}\\ \therefore Att=2s\\ v=3\hat{i}+8\hat{j}m/s\end{array}$

Similarly the acceleration is

$a=\frac{dv}{dt}=0+4\hat{j}$

Therefore, the acceleration is independent of $t$ and is a constant $4\hat{j}m/s^2$.