Derive an expression for kinetic energy of a moving body.
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. Derivation: Let us consider an object of m which is at rest lying on a table. Let A force F acts on the object which moves the object through a distance S. The workdone=F×S W=Fnet×S-------(1) Let the work done on the object causes a change in its velocity from u to V and let a be the acceleration. From Third equation of motion: V²−u²=2as s=V²−u²/2a----------(2) By Newton's Second law: F=ma------(3) From equation (1), (2) and (3) W=ma×(V2−u2/2a)=(1/2)m(V2−u2) As we assumed object at rest, u=0 W=(1/2)mV2 we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest. ∴K.E=1/2mV2
