Question

The potential energy of a 1kg particle free to move along the    x-axis is given by

V(x) = (x⁴/4 - x²/2)J

The total mechanical energy of the particle 2J.
Then, the maximum speed (in m/s) is
(a) 2 

(b) 3/√2

(c) √2 

(d) 1/√2 . 

Answer 1

(b) : Total energy E_T = 2J. It is fixed.
For maximum speed, kinetic energy is maximum
The potential energy shouldtherefore be minimum.