Derive an expression for kinetic energy of an object mass m moving with uniform velcoity v what happens to the kinetic energy of a body if its velcoity is halved?

To derive the expression for kinetic energy, we start with the definition of kinetic energy (K.E.):

K.E. = 1/2 * m * v^2

where m is the mass of the object and v is its velocity.

Now, let's answer the second part of the question. If the velocity of the body is halved, let's say the new velocity is v/2. We can substitute this new velocity into the kinetic energy equation:

New K.E. = 1/2 * m * (v/2)^2
= 1/2 * m * (v^2/4)
= 1/2 * m * v^2/4
= 1/8 * m * v^2

So, if the velocity is halved, the kinetic energy becomes 1/8 (one-eighth) of its original value.

To summarize:
- The expression for the kinetic energy of an object is K.E. = 1/2 * m * v^2.
- If the velocity of the body is halved, the new kinetic energy becomes 1/8 of its original value.

KE = 0.5M*V^2.

KE = 0.5M*(V/2)^2 = 0.5M*V^2/4.
So KE is reduced by a factor of 4(divided by 4).