What do you mean by kinetic energy derive an expression for the kinetic energy of an object moving with velocity V?

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define kinetic energy. derive an expression for kinetic energy?

Posted by Savitajain Jain 6 months, 1 week ago

The kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. 

Consider a body of mass "m" starts moving from rest. After a time interval "t" its velocity becomes V.
If initial velocity of the body is Vi = 0 ,final velocity Vf = V and the displacement of body is "d". Then

Derivation for the equation of Kinetic Energy: The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is 

                             v2 - u2 = 2aS

                             S = ½a(v2 - u2) 

                            W = ma × ½a(v2 - u2) 

                            W = ½mv2

If u = 0, the work done will be  W = ½mv2

Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek=  ½mv2

Define Kinetic Energy and derive the expression for it.

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$W=F.s$

where $F$ is the force and $s$ is the displacement in the direction of the force.

We know that, $F=ma$
Therefore, $W=m.a.s$ -------(1) From the equation of motion, we have,

$v^2-u^2=2as$

Therefore, $\frac{1}{2}{v}^2$ $=as$ ------- (2)

Therefore, $KE=\frac{1}{2}m{v}^2$.