Question

What is kinetic Energy?

Answer 1

Hint: A body possesses two kinds of energy; one of them is kinetic energy. Kinetic energy is always positive and a scalar quantity even though it depends on a vector quantity, velocity. Energy is stored in the body when work is done on it or used when work is done by it.

Formulas Used:
\[K=\dfrac{1}{2}m{{v}^{2}}\]

Complete answer:
Kinetic Energy is the energy possessed by a body due to its motion. The kind of motion may be translational, rotational, vibrations or can even be a combination of motions. When work is done on an object by a force, the object accelerates and gains kinetic energy. Kinetic energy depends on the mass and velocity of an object. Its SI unit is joules (\[J\]).
Kinetic energy can also be described as the work required to accelerate a body of a given mass from rest to the given velocity.
 Kinetic energy of a body of mass\[m\], moving with velocity\[v\]is given by,
\[K=\dfrac{1}{2}m{{v}^{2}}\]
\[1J\]is the kinetic energy possessed by a body of mass\[1\,kg\]moving with velocity\[1\,m{{s}^{-1}}\].
Kinetic Energy possessed by a body in rotational motion is given by-
\[{{E}_{rotational}}=\dfrac{1}{2}I{{\omega }^{2}}\]
here
\[I\] is moment of inertia of the body about its axis
\[\omega \] is the angular velocity.
Kinetic energy can be converted to different forms. For example- Due to friction, some of the kinetic energy is dissipated as heat.
We can derive kinetic energy as-
We know that,
The work done (\[E\]) to accelerate a mass m from its rest in time \[dt\] is given by-
\[E=Fdx\] - (1)
Here, \[F\] is the force required
\[dx\]is the displacement travelled in time\[dt\]
We know,
\[\begin{align}
  & v=\dfrac{dx}{dt} \\
 & \\
\end{align}\]
\[\Rightarrow vdt=dx\] - (2)
Substituting eq (2) in eq (1), we get,
\[E=Fvdt\]
Force is rate of change of momentum (\[p\]), \[F=\dfrac{dp}{dt}\] substituting in above eq
\[\begin{align}
  & E=v\dfrac{dp}{dt}\cdot dt \\
 & E=vdp=vd(mv)=m(vdv) \\
 & \\
\end{align}\]
Integrating the equation, we get,
\[\begin{align}
  & E=m\int{vdv} \\
 & \Rightarrow E=\dfrac{1}{2}m{{v}^{2}} \\
\end{align}\]
Therefore kinetic energy is the energy possessed by a body by virtue of its motion.

Note:
Kinetic energy can be converted to different forms. The kinetic energy in windmills and hydroelectric power plants is converted to electricity. It is the basis of many alternate sources of energy. Airplanes are able to fly because they possess high kinetic energy as they have a large mass and move with high velocities.