When a conservative force does positive work on a body,then the

$A$ particle of mass $m$ with initial kinetic energy $K$ approaches the origin from $x = +\infty$. Assume that a conservative force acts on it and its potential energy $V(x)$ is given by $V(x) = \frac{K}{\exp(3x/x_0) + \exp(-3x/x_0)}$, where $x_0 = 1 \ m$. The speed of the particle at $x = 0$ is

Assertion $(A) :-$ If work done by the force depends on the path,then the force is said to be non-conservative.
Reason $(R) :-$ All conservative forces are central forces.

Give examples of a conservative force and a non-conservative force.

The potential energy for a force field $\vec{F}$ is given by $U(x,y) = \cos(x + y)$. The force acting on a particle at the position given by coordinates $(0, \frac{\pi}{4})$ is

Is the work done by non-conservative forces always negative? Discuss.