Question

Derive kinetic energy

Answer 1

Start with the formula for work: work done = mf × s , where m = mass of the object, f = constant acceleration, and s = linear distance over which the force is applied. Relate velocity, acceleration, and distance by Applying the equation v² = u² + 2 fs where v is the terminal velocity of the object and u is the initial velocity . Assuming the object starts from rest, u = 0. Solve for acceleration to get a = v² / 2x. substitute into the equation for work done = m × v² / 2s × s = kinetic energy or kinetic energy ( k.e.) = 1/2 m v². Since the work required to accelerate an object exactly equals the kinetic energy imparted to it, this expression, 1/2 m v ², gives the energy in joules or ergs according to the system of units used above.

Answer 2

In short I am writing okay!

So 1st,

W = fs -----------(1)

F = ma-------------(2)

Now,

2as = v^2 – u^2 ( u = 0m/s)

S = v^2 / 2a -------------(3)

So putting (2) and (3) in eq.(1)

We get,

W = ma * v^2/2a

W = 1/2mv^2

 

I hope it helps………