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Proof the Expression for Kinetic energy.
Dear Student,
The equation of kinetic energy can be acquired from the equation of motion. Let us assume that an object of mass m is initially at rest and in time t it moves with velocity of v. Consider that the distance covered by the object is s thus from we know that distance s is related to average velocity and time as follows,
s=vav×ts=vav×t
That is,
s=v−u2×ts=v-u2×t
As initially the object is at rest, therefore we get,
s=vt2s=vt2
Newton’s second law of motion says that,
F=maF=ma
As, a=vta=vttherefore we get,
F=mvtF=mvt
The work done by any object is defined as the product of force and the displacement, therefore we have,
W=mvt×vt2W=12mv2W=mvt×vt2W=12mv2
Therefore, according to the definition of kinetic energy the net work done is the change in kinetic energy of the object, therefore have,
KE=12mv2KE=12mv2
Regards
The equation of kinetic energy can be acquired from the equation of motion. Let us assume that an object of mass m is initially at rest and in time t it moves with velocity of v. Consider that the distance covered by the object is s thus from we know that distance s is related to average velocity and time as follows,
s=vav×ts=vav×t
That is,
s=v−u2×ts=v-u2×t
As initially the object is at rest, therefore we get,
s=vt2s=vt2
Newton’s second law of motion says that,
F=maF=ma
As, a=vta=vttherefore we get,
F=mvtF=mvt
The work done by any object is defined as the product of force and the displacement, therefore we have,
W=mvt×vt2W=12mv2W=mvt×vt2W=12mv2
Therefore, according to the definition of kinetic energy the net work done is the change in kinetic energy of the object, therefore have,
KE=12mv2KE=12mv2
Regards