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Physics · LAWS OF MOTION
हिन्दीA time-dependent force \( \vec{F} = (6 t \hat{i} + 4 t^2 \hat{j})\text{ N} \) acts on a particle of mass \( 2\text{ kg} \) which is initially at rest at \( t = 0 \). The speed of the particle at \( t = 3\text{ s} \) is:
Correct answer · Option 2
22.5 m/s
Explanation
Acceleration \( \vec{a} = \frac{\vec{F}}{m} = (3t \hat{i} + 2t^2 \hat{j})\text{ m/s}^2 \). Integrating gives \( \vec{v}(3) = [ \frac{3t^2}{2} \hat{i} + \frac{2t^3}{3} \hat{j} ]_0^3 = (13.5 \hat{i} + 18 \hat{j})\text{ m/s} \). Speed \( |\vec{v}| = \sqrt{13.5^2 + 18^2} = 22.5\text{ m/s} \).
