A block of mass 2 kg is kept at origin at t = 0 and is having velocity 4 5 m / s in positive x - direction. The only force on it is a conservative and its potential energy is defined as U = - x 3 + 6 x 2 + 15 ( SI units). Its velocity when the force acting on it is minimum (after the time t = 0 ) is

Question

A block of mass 2 kg is kept at origin at t = 0 and is having velocity 4 5 m / s in positive x - direction. The only force on it is a conservative and its potential energy is defined as U = - x 3 + 6 x 2 + 15 ( SI units). Its velocity when the force acting on it is minimum (after the time t = 0 ) is, 8 m / s, 4 m / s, 10 24 m / s, none of these

MARKS App · Accepted Answer

At x = 0 K = 1 2 × 2 × 80 = 80 J and U = 15 J ∴ Total energy is, E = K + U = 95 J Force, F = - dU dx ⇒ F = 3 x 2 - 12 x For F to be minimum, dF dx = 0 ⇒ x = 2 m At x = 2 m E = K + U ⇒ 95 = 1 2 × 2 × v 2 + - 8 + 24 + 15 ⇒ v = 8 m / s

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