What is the acceleration of a particle at x=10 m if the mass of the particle is 0.2 kg ?the particle is moving along x axis with the potential...

Work is given by the product of the force and distance.
The work done contributes to an increase in potential
energy.

Work = -delta
U.

Force* distance = -delta
U

Here we have the function of the potential energy given
as U(x) = 8*x^2 - 2*x^4.

For an infinitesimally small
change in distance

d/dx (Force* distance) =
-U'(x)

Force = -U'(x)

U'(x) =
16x - 8x^3

At x = 10,

U'(x) =
16*10 - 8*1000

=> 160 -
8000

=> -7840

=>
Force = - (-7840)

=> Force =
7840

So the force at this point is
7840.

Force is the product of the mass and acceleration. We
know that the mass is 0.2 kg.

Therefore the
acceleration is 7840 / 0.2 = 39200 m/s^2