Question

of an
derive the formula for the kinectic.
energy
object of mass
of mass m moving
velocty. v.:
[expression for kinetic energy, en suppose
to ke = 1 my 2
2​

Answer 1

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Drive the formula for the kinetic energy of an object of mass m moving with velocity v [Expression for kinetic energy suppose KE = 1/2mv²]

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Let us considered a block of mass kept at rest on a friction less surface. let a constant F applied on a block.

The work done on the block by the force F is

$\bf\:w=f\times\:s$

$\bf\:w=m\times\:a\times\:s..............(i)$

Now,

$\bf\implies\:{v}^{2}={u}^{2}+2as$

$\bf\implies\:{v}^{2}={0}^{2}+2as$

$\bf\implies\:{v}^{2}=2as$

$\bf\implies\:a=\dfrac{{v}^{2}}{2s}...........(ii)$

From equation (i) and (ii)

$\bf\:=m\times\:\dfrac{{v}^{2}}{2s}\times\:s$

$\bf\:=\dfrac{1}{2}m{v}^{2}$

$\bf\pink{{\therefore\:W=KE=\dfrac{1}{2}m{v}^{2}}}$

☛Kinetic energy :- Energy possess by a body due to its motion is known as kinetic energy.