For a system of conservative forces,the potential energy $U$ is given by the formula $U = ax^2 - bx$,where $a$ and $b$ are constants. Determine the force $F$.

Give three definitions of conservative force.

If $F = 2x^2 - 3x - 2$,then choose the correct option.

$A$ body with mass $2\, kg$ moves in one direction in the presence of a force which is described by the potential energy graph. If the body is released from rest at $x = 2\, m$,then its speed when it crosses $x = 5\, m$ is ................ $m/s$.

Potential energy is defined ............

Obtain the relation between potential energy and force for a conservative force.