The velocity of a body moving in a strai | Class 9 Science Chapter Work and Energy, Work and Energy NCERT Solutions

Question:

The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.

Answer:

Let a body of mass changes its velocity from "u" to "v"  with an acceleration, "a" due to the application of a constant force, "F" in the direction of motion, then the  displacement of the body, "S" is given by ⇒S = (v2 - u2)/2a, but the work done in changing the velocity of the body from u to v is W = F.S

W = ma[(v2 - u2)/2a]
W = m[(v2 - u2)/2]
W = m/2[v2 - u2]
W = m/2(v2) - m/2(u2)
W = 1/2(mv2) - 1/2(mu2),
But  1/2(mv2) - 1/2(mu2) = Change in kinetic energy So, Change in kinetic energy = W = 1/2(mv2) - 1/2 (mu2).


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Welcome to the NCERT Solutions for Class 9 Science - Chapter . This page offers a step-by-step solution to the specific question from Excercise 0 , Question 17: The velocity of a body moving in a straight line is increased by applying a constant force F, for so....