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Physics · LAWS OF MOTION
हिन्दीA time-dependent force \( \vec{F}(t) = (A t - B t^2)\hat{i} \) acts on a particle of mass \( m \) initially at rest from \( t = 0 \) to \( t = \frac{A}{B} \), where \( A \) and \( B \) are positive constants. The final velocity acquired by the particle at \( t = \frac{A}{B} \) is:
Correct answer · Option 3
\( \frac{A^3}{6 m B^2} \)
Explanation
Impulse \( I = \int_0^{A/B} (At - Bt^2) dt = [ \frac{A t^2}{2} - \frac{B t^3}{3} ]_0^{A/B} = \frac{A^3}{6 B^2} \). Velocity \( v = \frac{I}{m} = \frac{A^3}{6 m B^2} \).
