Question

Define kinetic energy give its mathematical expression

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

• Let the body's mass be "m"
• Moving with a initial velocity "u".
• And, Covers a distance "s".
• Therefore, reaches final velocity "v".

$\huge{\bold{\underline{Explanation:-}}}$

Kinetic energy:-

• Kinetic energy is the energy that is possessed by a body due to virtue of its motion.
• It is a form of mechanical energy.
• S.I units :- Joules / CGS units :- ergs.

Derivation of Kinetic energy.

From third kinematic equation.

$\large{\bold{v^2 - u^2 = 2as}}$

Multiply with $\large{ \dfrac{1}{2}. m}$ on both sides.

Therefore,

$\large{ \implies \dfrac{1}{2} .m\times (v^2 - u^2) = \dfrac{1}{2}.m \times 2as}$

$\large{ \implies \dfrac{1}{2} \times (v^2 - u^2) = \dfrac{1}{ \cancel{2}}. m \times \cancel{2}as}$

$\large{ \implies \dfrac{1}{2} \times (v^2 -u^2) = mas}$

As we know,

$\large{F = ma}$

Substituting,

$\large{ \implies \dfrac{1}{2} \times m \times (v^2 - u^2) = F.s}$

As we know,

$\large{W = F.s}$

$\large{ \implies \dfrac{1}{2} \times m \times (v^2 - u^2) = W}$

Since, the body is moving,

therefore the Kinetic energy equals the work done.

$\large{ \implies \dfrac{1}{2} \times m \times (v^2 - u^2) = K.E}$

Rearranging,

$\huge{\boxed{\boxed{K.E = \dfrac{1}{2}m(v^2 - u^2)}}}$

Note:-

If the initial velocity is Zero.

then,

$\large{\bold{K.E = \dfrac{1}{2}mv^2}}$

Units of Kinetic energy is Joules.

Answer 2

Explanation:

W=(1/2)mV2. we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.