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Physics · MOTION IN A PLANE
हिन्दीA particle's position vector as a function of time \( t \) is given by \( \mathbf{r}(t) = (3t^2 - 2t)\hat{i} + (4t - 5)\hat{j} \) in SI units. What is the magnitude of the average velocity vector between \( t = 1\text{ s} \) and \( t = 3\text{ s} \)?
Correct answer · Option 1
\( 2\sqrt{29}\text{ m/s} \)
Explanation
At \( t = 1\text{ s} \), \( \mathbf{r}(1) = 1\hat{i} - 1\hat{j} \). At \( t = 3\text{ s} \), \( \mathbf{r}(3) = 21\hat{i} + 7\hat{j} \). Displacement \( \Delta\mathbf{r} = 20\hat{i} + 8\hat{j} \). Average velocity \( \mathbf{\bar{v}} = \frac{20\hat{i} + 8\hat{j}}{2} = 10\hat{i} + 4\hat{j} \). Magnitude \( |\mathbf{\bar{v}}| = \sqrt{10^2 + 4^2} = \sqrt{116} = 2\sqrt{29}\text{ m/s} \).
