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Question
A body of mass m is moving with a velocity v. Write the expression for its kinetic energy.
Solution
Assume that a mass-m body is travelling at a velocity of v. An opposing force, F brings it to rest.
Let a represent the force's uniform retardation, and let it travel a distance of S before coming to rest at T. Then,
The kinetic energy of the body = the work done by the retarding force in stopping it.
Kinetic energy = Force × displacement
= F × S ...(i)
Retarding force F = ma ...(ii)
Initial velocity u = v, final velocity v = 0
From the relation v2 = u2 +2aS
0 = v2 - 2aS (since a is the retardation)
∴ Displacement S = `v^2/(2a)` ...(iii)
Substituting the values of F and S from equation (ii) and (iii) in equation (i), we get
kinetic energy `K = F × S = ma × v^2/(2a) = 1/2 mv^2`
Kinetic energy = `1/2 ` mass × (velocity)2
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