derive the equation Ek 1/2mv2
Answers
Answer:
The formula Ek=1/2mv^2 derives from Ek=mas. ... KINETIC energy, Ek = ½mv^2 where m is mass and v is velocity
Answer:
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,
V2 = u2 + 2as
or s = v2 -u2 / 2a ----------------------------- 2
The work done by the force
W = F x s -------------------------------------- 3
Substituting 1 and 2 in 3
W = (m x a) x (v2 - u2/2a)
W = m/2 (v2 - u2)
W = 1/2 mv2 - 1/2 mu2 -------------------- 4
For an object to be at rest in the beginning, u = 0
Therefore, W = 1/2 mv2
W = Ek ( Ek = kinetic energy)
Therefore, Ek = 1/2 mv2