If the speed of a particle triples ,by what factor does its kinetic energy increase?

Kinetic energy = (1/2) (mass) (speed)²  .

See that little ² there on the end ?  That tells us that kinetic energy is proportional to the square of the speed.

If the speed of the moving object triples, then the moving object has 3² or nine times as much kinetic energy as it had before.

A better way to look at it is:  If you want to triple the speed of a moving object, it's not enough to just give it 3 times as much kinetic energy as it has now.  You have to give it 9 times as much as it has now.

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