Question

Question :-
Derive kinetic energy formula by algebra method.

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Answer 1

☯ Kinetic Energy :-

The energy possessed by a body be virtue of its motion is called as Kinetic energy .

♦ K.E = 1/2 × mv² ♦

★ Deriving the formula :-

By observing the given figure in the attachment ,

• The body is at rest , a force F applied on the body of mass m , then it moves with answer acceleration of a , then it moves with a velocity v and travelled a distance S.

So ,

→ W = F.S

→ W = ma.S ...eq(1)

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⇒ v² - u² = 2as

⇒ v² = 2as [ °.° u = 0 ]

⇒ a = v²/2S

Substituting the value of a in eq(1)

⇒ W = m [ v²/2S ] .S

⇒ W = m [v²/2]

⇒ W = 1/2 mv²

So , here the work done considered as K.E.

⇒ K.E. = 1/2 mv²

Hence , derived !

Answer 2

$\sf{Solution}$

Step-by-step-explanation:-

We have to derive the formula of Kinetic energy by algebra method !

Solution :-

First we will know the definition of Kinetic energy and formula

Kinetic energy :-

The energy possessed by a body by virtue of its motion is known as kinetic energy

K.E = $\sf\dfrac{1}{2}$mv²

Derivation :-

Consider a body of mass m which is intially at rest moving along a straight line with a velocity v the application of constant force F Let the displacement is S

Work done by Force F

W = F .S (∴θ = 0°)

If a is the acceleration produced then according to Newton seconds law

F = ma

∴ W = FS = mas _____ 1

By the equations of motion we know that

v² - u² = 2as

v² - 0² = 2as

v² = 2as

S = $\sf\dfrac{v²}{2a}$ ________2

Substuite eq 2 in eq 1

W = mas

= ma $\sf\dfrac{v²}{2a}$

W = $\sf\dfrac{mv²}{2}$

W = $\sf\dfrac{1}{2}$mv²

But the Kinetic Energy of a body is equivalent to work is giving body this velocity

Hence K.E = $\sf\dfrac{1}{2}$mv²

Hence derived!!

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Since both m& v² are always positive .K.E is always positive It direction depends on motion

Kinetic energy depends on frame of reference

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Hope u helpful