Question

What is kinetic energy ?deduce an expansion for kinetic energy of a body of mass M and moving with a velocity v

Answer 1

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Answer 2

Energy possessed by an object due to its motion is called kinetic energy.

Consider an object of mass M , moving with an uniform velocity u. Let it be displaced through a distance s when a constant force F acts on it in the direction of its displacement . The work done on the object will cause a change in its velocity. Let the work done be W

W = Fs ---------- (1)

Let its velocity change from u to v . Let a be the acceleration produced.

We know that,

v² - u² = 2as

s = v² - u²/2a ----------(2)

According to newton's second law of motion,

F = ma ------------(3)

Substituting eq. (2) and (3) in eq. (1),

W = ma × (v² - u²/2a)

W = m × (v² - u²/2)

W = 1/2 m (v² - u²)

If the object is starting from stationary position then u = 0

W = 1/2 mv²

Work done = energy stored

Here, work done = kinetic energy

Therefore, Kinetic energy = 1/2 mv²

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