If the momentum of an object is increased by four times, then what will be its final kinetic energy?

Momentum, or impulse (the change in momentum) of an object is its "quantity of motion." It is defined as the product of the mass `m` of an object and its velocity `V.` As such, momentum is actually a vector quantity.

When two bodies move towards one another and have a collision, the object which has a greater momentum hits harder. Also, for a closed system of bodies, momentum is conserved.

Kinetic energy is a scalar quantity which is defined as `(mV^2)/2.` It is also a measure of a quantity of a body's motion. Energy (not only kinetic but all types of energy) is also conserved in a closed system.

Now if `mV` is increased `4` times (and mass `m` remains the same), this means `V` is increased `4` times: `V_1=4V.` Therefore, kinetic energy becomes `(mV_1^2)/2=(m(4V)^2)/2=16*(mV^2)/2.`

So, we can state that kinetic energy is increased `4^2` = 16 times. This is the answer.