Question

A single conservative force f(x) acts on a 1.0 kg particle that moves along x axis. the potential energy u(x) associated with f(x) is given by u(x) = j, where x is in meters. at x=5.0m the particle has a kinetic energy of the2.0j. what is the acceleration of the particle at x= 5.0 m?

Answer 1

The acceleration of the particle at x=5.0m is 0.

Step-by-step explanation:

The potential energy associated with the force f(x) is given by u(x) = j.

At x = 5.0m, the particle has a kinetic energy of 2.0J.

Since the total mechanical energy E of the particle is the sum of its potential energy and kinetic energy, we can write:

E = u(x) + K.E.

Given that K.E. = 2.0J and u(x) = j, we can substitute the values into the equation:

-6.0J = j + 2.0J

Solving for j, we find j = -8.0J.

Since force is the derivative of potential energy with respect to displacement, we can find the force at x = 5.0m by taking the derivative of u(x) = j:

f(x) = -∂u(x)/∂x = -∂j/∂x = 0

Therefore, the acceleration of the particle at x = 5.0m is 0.