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?
See previous post.
To derive an expression for the kinetic energy of an object moving with uniform velocity, we'll start with the definition of kinetic energy.
The kinetic energy (K) of an object is given by the formula:
K = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.
Now, let's move on to the second part of your question. If the velocity of a body is halved, we need to find out what happens to the kinetic energy.
Let's consider the initial kinetic energy of the body as K1 when its velocity is v, and the final kinetic energy as K2 when its velocity is halved, which becomes v/2.
Using the formula for kinetic energy, we can write:
K1 = (1/2) * m * v^2
K2 = (1/2) * m * (v/2)^2
Simplifying the equation for K2:
K2 = (1/2) * m * (v^2/4)
K2 = (1/8) * m * v^2
Therefore, when the velocity is halved, the kinetic energy becomes (1/8) times the initial kinetic energy.
So, the kinetic energy reduces to one-eighth of its original value when the velocity of an object is halved.