$A$ particle of mass $1 \ kg$ is free to move along the $x$-axis. Its potential energy is given by $U(x) = (\frac{x^2}{2} - x) \ J$. If the total mechanical energy of the particle is $2 \ J$,find the maximum speed of the particle.

Potential energy is a......

$A$ particle with constant total energy $E$ moves in one dimension in a region where the potential energy is $U(x)$. The speed of the particle is zero where

The force acting on a particle is given by the formula $F(x) = -kx + ax^3$. Find the graph of its potential energy $U(x)$ for $x \ge 0$.

The potential energy $(U)$ of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $U = \frac{\alpha}{r^{10}} - \frac{\beta}{r^5} - 3$,where $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be $\left(\frac{2\alpha}{\beta}\right)^{\frac{a}{b}}$,where $a = \dots \dots \dots \dots$

While a person climbs stairs,the gravitational potential energy of the person increases. The source of this energy is