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The kinetic energy of an object with mass m and which has a speed of v is given by (1/2)*m*v^2.
The change in the kinetic energy of the object as the speed changes is proportional to the square of the factor by which the speed changes. For example if the speed of the object becomes double, its kinetic energy changes to four times the initial kinetic energy. Similarly, if the speed of the object triples the kinetic energy becomes nine times the initial kinetic energy.
If the speed of an object changes by a factor k, the change in the kinetic energy is of a factor k^2.
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