How does kinetic energy change if momentum is increased by 3times?

Solution
We know,

KE = ½ mv2

P = mv

Therefore, KE = ½ (mv)2/m = p2/(2m)

Considering the mass to be constant, if the momentum is increased by 3 times,  the new momentum be,

P/ = 3P

The new kinetic energy is, KE/ = (P/)2/(2m)

=> KE/ = (32)[P2/(2m)] = 9 KE


So kinetic energy becomes 9 times

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