Question

divert the formula of kinetic energy

Answer 1

Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared. Hope it helps you....

Answer 2

Suppose, the mass of a moving object = m

The initial velocity of a moving object = u

The acceleration of the object = a

The final velocity of the object = v

Displacement of object to achieve the final velocity = s.

We know from the equation of motion that,

v2=u2+2asv2=u2+2as

⇒2as=v2−u2⇒2as=v2-u2

⇒s=v2−u22a⇒s=v2-u22a -----(i)

Now, we know that, Work done, W=F×sW=F×s

Thus, by substituting the value of ‘s’ from equation (i) in the expression W = F x s, we get

W=F×v2−u22aW=F×v2-u22a

Now, according to Newton’s Second Law of motion, Force = mass x acceleration

Or, F = m x a

Therefore, by substituting the value of F in equation (ii) we get,

W=m×a×v2−u22aW=m×a×v2-u22a

⇒W=12m(v2−u2)⇒W=12m(v2-u2) ---(iii)

If the object starts moving from the state of rest, therefore, initial velocity (u) will be equal to zero.

Therefore, equation (iii) can be written as

⇒W=12m(v2−02)⇒W=12m(v2-02)

⇒W=12mv2⇒W=12mv2 ------(iv)

Equation (iv) shows that work done is equal to the change in kinetic energy of an object.

Therefore, if an object of mass ‘m’ is moving with a constant velocity,

Thus, the Kinetic Energy (Ek)=12mv2(Ek)=12mv2 ----(v)