The kinetic energy of a body is related to its mass and velocity by the following relationship:

Kinetic energy = `1/2 mv^2`

where, m is mass of the body (or object) and v is its velocity. Hence the kinetic energy is directly proportional to the mass of body and square of velocity.

When the velocity of the object is tripled, that is, new velocity is three times the original velocity, or v' = 3v, the new kinetic energy would be

K.E.' = `1/2 mv'^2 = 1/2 m(3v)^2 = 1/2 m(9v^2) = 9 [ 1/2 mv^2]`

Thus, the new kinetic energy is **9 times** the original kinetic energy.

From this case, we can see that a small change in velocity can result in large changes in kinetic energy of the object. We can relate this case to driving. Imagine accelerating from 20 miles per hour to 60 miles hour and your car now has 9 times the original kinetic energy.

Hope this helps.

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