Question

Derive the formula for Kinetic energy.

Answer 1

Answer:

EK =1/2 mv²

EK=et+er

derive formula for kinetic energy

Answer 2

According to me :-

Derivation of the equation for kinetic energy:

Expression for Kinetic energy(Ek)-

Consider an object with mass m, moving with initial velocity u. Let a force F, act on it causing a displacement s, along the direction of force and accelaration. Let the object attain final velocity v.

We know F = m x a ------------------------ 1

By position velocity relation we have,

V^2 = u^2 + 2as

or s = v^2 -u^2 / 2a ----------------------------- 2

The work done by the force

W = F x s -------------------------------------- 3

Substituting 1 and 2 in 3

W = (m x a) x (v^2 - u^2/2a)

W = m/2 (v^2 - u^2)

W = 1/2 mv^2 - 1/2 mu2 -------------------- 4

For an object to be at rest in the beggining, u = 0

Therefore, W = 1/2 mv^2

W = Ek ( Ek = kinetic energy)

Therefore, Ek = 1/2 mv^2

《 in short 》

Algebra Derivation:

∆KE=Fd

∆KE=mad (recall that F=ma)

Now, we use the kinematic equation: vf^2-vi^2= 2ad and solve for ad, then we substitute into the original equation.

∆KE=m((vf^2-vi^2)/2)

(vf is final velocity and vi is initial velocity)

We finally expand to get:

∆KE=1/2 mvf^2–1/2mvi^2