Question

The potential energy of a particle of mass 1 kg moving along x-axis given by U(X) =
If total mechanical energy of particle is 2 J, then find its maximum speed.​

Answer 1

Answer:

Explanation:

=> Here, The potential energy of a particle of mass 1 kg moving along x-axis given by U(X) =[x⁴/4−x²/2] J

=> Now, when Kinetic energy of the particle is maximum and potential energy is minimum, velocity is maximum.

∴ dV/dx = 0

x³ - x = 0

x = ± 1

For the minimum potential energy, x = 1

minimum potential energy =1/4−1/2=−1/4J

=> According to question,

Total M.E = K.Emax+P.Emin = 2J

KEmax = 2 + 1/4 = 9/4

9/4 = 1/2mv²max                     (m=1kg)

v²max = 9*2/4

v²max = 9/2

vmax = 3√2 m/s

Thus,  its maximum speed is 3√2 m/s.