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Kinetic energy is directly proportional to the square of an object's velocity.

If you graph the object's kinetic energy against the square of its speed, the

graph is a straight line, and the slope of the line is 1/2 of the object's mass.

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12y ago
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13y ago

This goes back to the derivation of kinetic energy.

Consider a body of mass m, initially at rest, being accelerated by a constant force F to a speed v through a distance s.

The acceleration produced by the force is given by

a = F/m

Applying Newton's equation of motion v2 = u2 +2as, we have

v2 = 0 +2(F/m)s

Fs = 1/2 mv2

The work done by the force, Fs, is completely converted into the kinetic energy of the body.

Thus kinetic energy = 1/2 mv2

This is where the v2 comes from.

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