Question

Find the correctness of KINETIC ENERGY=1/2 mv^2

Answer 1

Answer:

Kinetic Energy(K)= the work against

F force

= F. s = ma .s ..... (i)

for a particle

final velocity(V)= 0

we know,

$= > {0}^{2} = {u}^{2} - 2as$

$=> 2as = {u}^{2}$

$=> as = \frac{ {u}^{2} }{2}$

from (i)no. K = m. u^2/ 2

if u = v, K= 1/2mv^2

Answer 2

              Kinetic energy =  $\frac{1}{2}\ mv^{2}$

_____________________

Let initial velocity = u

Let applied force = F.

Acceleration = a

Time = t

Displacement during time = s

Final velocity = v

______________________

According to the 2nd law of motion,

F = ma -------- (i)    (Work done on an object W = F * s)

By using 2nd equation of motion,

S = ut + 1/2 at²  (But, Initial velocity is 0)

S = 0 + 1/2 at²

Therefore,

S = 1/2 at² ------------ (ii)

Adding equation (i) and (ii)

W = ma * 1/2 at²

∴ W = 1/2 m(at)² ------------- (iii)

Now, By using first equation of Motion,

V = u + at [ (U) Initial velocity is 0]

V = 0 + at

V = at

∴ V² = at² -------------- (iv)

From equation (iii) and (iv)

W = 1/2 mv²

We know that, Work done by an object is equal to it's Kinetic Energy.

i.e. K.E = W

Therefore,

                             Kinetic Energy = 1/2 mv²