A block of mass 2 k g is kept at the origin at t = 0 and is having velocity 4 5 m s - 1 in the 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 . Its velocity when the force acting on it is minimum (after the time t = 0 ) is -

Step-by-step solution

At x = 0 K = 1 2 × 2 × 80 = 80   J and U =   15   J ∴   E =   K + U =   95   J F = - d U d x ⇒ F = 3 x 2 - 12 x For F = m i n i m u m ,   d F d x = 0 ⇒   x = 2   m At x   = 2   m E =   K + U ⇒   95 = 1 2 × 2 × v 2 + - 8 + 24 + 15 ⇒ v =   8   m   s - 1