Prove that the increase in kinetic energy of a body=work done by the force on the body.The velocity of the body is increased by applying a constant force for some distance in the direction of motion.

Asked by aahnik.mohanty | 19th Dec, 2017, 09:13: PM

Expert Answer:

(Note :-  Vectors are typed as Bold letters)

Workdone = Force × distance =
 
Force F = Rate of change of momentum = m(vf - vi)/t
 
m - mass of object, vf and vi are final and initial velocity respectively. t is time taken for the velocity change.
 
distance travelled in time t = t × (vf+vi)/2
 
Hence workdone = [ m(vvi)/t ] • [t × (vvi)/2 ]  = (1/2)×m× (vf-vi) • (vf+vi) = (1/2)×m×(vf- vi2) = change in kinetic energy

Answered by  | 20th Dec, 2017, 11:13: AM