Work done by a constant force $\vec{F}$ for displacing an object by a displacement of $\Delta \vec{x}$ is given by,

$\Delta W=\vec{F} \cdot \Delta \vec{x}=F \Delta x \cos \theta$

Work done by a variable force $\vec{F}$ for displacing an object from $x=x_1$ to $x=x_2$ is given by :

$W=\int_{x_1}^{x_2} \vec{F} \cdot d \vec{x}$

Energy is a number that we associate with a system of one or more objects. This number which we call energy can be transformed from one form to another and transferred from one object to another, but the total amount is always same. And this energy is transferred by only one way called work.

Kinetic energy of an object of mass $m$ and moving with a velocity of $\vec{v}$ is given by:

$$ \mathrm{K} . \mathrm{E} .=\frac{1}{2} m \vec{v} \cdot \vec{v}=\frac{1}{2} m v^2 $$

Change in the kinetic energy of a particle = Net work done on the particle

$W_{net}=K_2-K_1$

Gravitational potential energy of an object of mass $m$, at a height of $h$ above the reference level,

$\Delta U=m g h$

Potential energy of a spring when it is compressed or stretched by a length $x$ from its natural length,

$\Delta U=\frac{1}{2} k x^2$

Change in potential energy (ΔU) is negative of the work done by the conservative forces, that is ΔU = –W.

Average power, $P_{\mathrm{av}}=\frac{\Delta W}{\Delta t}$

Instantaneous power, $P=\frac{d W}{d t}=\vec{F} \cdot \vec{v}$