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Physics · LAWS OF MOTION
हिन्दीThe position of a particle of mass \( 2\text{ kg} \) moving along the x-axis is given by \( x(t) = 2 t^3 - 3 t^2 + 4 \) (where \( x \) is in meters and \( t \) in seconds). The magnitude of the impulse delivered to the particle between \( t = 1\text{ s} \) and \( t = 3\text{ s} \) is:
Correct answer · Option 1
72 N s
Explanation
Velocity \( v(t) = \frac{dx}{dt} = 6t^2 - 6t \). At \( t_1 = 1\text{ s} \), \( v_1 = 0\text{ m/s} \). At \( t_2 = 3\text{ s} \), \( v_2 = 6(3)^2 - 6(3) = 36\text{ m/s} \). Impulse \( J = m(v_2 - v_1) = 2(36 - 0) = 72\text{ N s} \).
