A block of mass 2 kg is at the origin at t = 0 and is having velocity 4 5 m s - 1 in the positive x-direction. The only force acting on it is a conservative and its potential energy is defind as U = – x 3 + 6 x 2 + 15 (SI units). Its velocity when its acceleration is minimum after t = 0 is-

Question

A block of mass 2 kg is at the origin at t = 0 and is having velocity 4 5 m s - 1 in the positive x-direction. The only force acting on it is a conservative and its potential energy is defind as U = – x 3 + 6 x 2 + 15 (SI units). Its velocity when its acceleration is minimum after t = 0 is-, 8 m s - 1, 4 m s - 1, 24 m s - 1, 20 m s - 1

MARKS App · Accepted Answer

F = – d U d x ⇒ F = 3 x 2 – 12 x Now F = m i n . ⇒ d F d x = 0 ⇒ x = 2 m U i + K i = U f + K f 15 + 1 2 × 2 × 80 = - 2 3 + 6 × 2 2 + 15 + 1 2 × 2 × v 2 v 2 = 64 v = 8 m s - 1

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