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Physics · MOTION IN A PLANE
हिन्दीA particle has an initial velocity \( \mathbf{v}_0 = (4\hat{i} + 3\hat{j})\text{ m/s} \) and a constant acceleration \( \mathbf{a} = (-2\hat{i} + \hat{j})\text{ m/s}^2 \). At what time \( t \) will the instantaneous velocity vector \( \mathbf{v}(t) \) be perpendicular to its initial velocity vector \( \mathbf{v}_0 \)?
Correct answer · Option 1
\( 5.0\text{ s} \)
Explanation
\( \mathbf{v}(t) = (4 - 2t)\hat{i} + (3 + t)\hat{j} \). Perpendicular condition: \( \mathbf{v}(t) \cdot \mathbf{v}_0 = 0 \implies 4(4 - 2t) + 3(3 + t) = 0 \implies 16 - 8t + 9 + 3t = 0 \implies 25 - 5t = 0 \implies t = 5\text{ s} \).
