Question

prove that the kinetic energy of a body of mass M moving with velocity given by 1/ 2 MV square and E K is equal to 1/2 MV square​

Answer 1

K E = 1/2×mv²

Explanation:

let a body is moving with a acceleration 'a' and started with initial velocity U reached to final velocity V and covered a distance S.

so ,from third equation of motion

V ² = u²+ 2 as

V ² - u² =  2 as

(V ² - u²)/ 2a=s

so it means,s=v2-u2/2a (1)

now you know that work done  is force*displacement

w= f×s                // force = mass*acceleration

w=m×a×s

putting the value of 's' from (1) ,

w=ma×(V ² - u²)/ 2a

w=m×(V ² - u²)

now we know that the object is started with the initial velocity zero so the value of u will be zero

putting the value of u=0

w=mv2/2

work energy theoram says work donr = change in  K E .

Ek=1/2×mv2