Question

The position of a particle is given by $\overrightarrow{r}=2t^2\hat{i}+3t\hat{j}+4\hat{k},$ where $t$ is in second and the coefficients have proper units for $\overrightarrow{r}$ to be in metre. The $\overrightarrow{a}(t)$ of the particle at $t=1s$ is

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

Answer 1

Answer: (C)

Distance, $\overrightarrow{\mathbf{r}}=2t^2\hat{\mathbf{i}}+3t\hat{\mathbf{j}}+4\hat{\mathbf{k}}$
Velocity, $\overrightarrow{\mathbf{v}}=\frac{\overrightarrow{\mathbf{dr}}}{dt}=4t\hat{\mathbf{i}}+3\hat{\mathbf{j}}$
Acceleration, $a=\frac{dv}{dt}=4\hat{\mathbf{i}}$
$=4m/s^2$ in the $x-$ direction.