A block of mass 2 kg 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…

Question

A block of mass 2 kg 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+6x^2+15. Its velocity when the force acting on it is minimum (after the time t=0 ) is -

MARKS Content Team · Accepted Answer

Correct answer: 8. At x=0 K=1/2×2×80=80 J and U= 15 J ∴ E= K+U= 95 J F=(-dU)/dx⇒F=3x^2-12x For F=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^(-1)

Solution

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