Question

Check whether the equation given below is consistent or not (correctness of the equation) ° kinetic energy = 1/2 mv^2

Answer 1

Answer:

Yes, its correct.

K. E. = 1/2 mv^2

Explanation:

The kinetic energy derivation using only algebra is one of the best ways to understand the formula in-depth.

Starting with the work-energy theorem and then adding Newton’s second law of motion we can say that,

∆K = W = F∆s = ma∆s (F = ma)

....... (i)

Now, taking the kinematics equation and rearranging it, we get,

v^2 = (Vo)^2 + 2a∆s

➡ 2a∆s = v^2 - (Vo)^2

➡ a∆s = (v^2 - (Vo)^2) / 2

..... (ii)

Combining the 2 expressions we get, that is from equation (i) and equation (ii),

➡ ∆K = m • (v^2 - (Vo)^2) / 2

➡ ∆K = (mv^2 / 2) - [m(Vo)^2 / 2]

Now we already know that kinetic energy is the energy that it possessed due to its motion. So the kinetic energy at rest should be zero.

Then, Vo = 0

Then, [m(Vo)^2 / 2] = 0

Therefore we can say that kinetic energy is:

➡ ∆K = (mv^2 / 2) - 0

➡ ∆K = (mv^2 / 2)

➡ ∆K = (1/2) × mv^2

Hence, the formula is verified.