Question

The position vector of an object at any time t is given by $3t^2 \hat{i} + 6 \hat{j} + \hat{k}$. Its velocity along Y-axis has the magnitude

• A. 6t
• B. 6
• C. 0
• D. 9

Answer 1

Answer: (C)

0

Answer 2

The position vector is

$$\vec{r}(t)=3t^2\,\hat{i}+6\,\hat{j}+\hat{k}.$$

Differentiate with respect to $t$ to get the velocity:

$$\vec{v}(t)=\frac{d\vec{r}}{dt}=6t\,\hat{i}+0\,\hat{j}+0\,\hat{k}.$$

The component along the $Y$-axis is zero, hence its magnitude is 0.