# 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 energy U(x)= 8x^2-2x^4

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### 2 Answers

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**

The acceleration is the ratio of the force and the unit mass.

Since we know the potential energy, we'll determine the intensity that is the same as acceleration.

dU/dx = d(8x^2-2x^4)/dx

dU/dx = 16x - 8x^3

Now, we'll substitute x by 10 m:

T = dU/dx

T = 16*10 - 8*10^3

T = 160 - 8000

**T = a = -7840 m/s^2**