Momentum is the total motion possessed by a body. Mathematically momentum can be represented by the formula:
Momentum = Mass*Velocity
This means that the momentum is directly proportional to the speed or velocity. Thus if the speed of an object is increased n times, its momentum will also be increased n times.
Kinetic energy of an objects refers to the energy that it possesses because of its motion, or velocity. This kinetic energy can be calculated by the formula:
Kinetic energy = (mass*Velocity^2)/2
This means that the kinetic energy is directly proportional to the square of speed or velocity. Thus if the speed of an object is increased n times, its kinetic energy will be increased n^2 times.
In the question given above the velocity of the object is increase 4 times. Therefore its momentum will also increase 4 times, and its kinetic energy will increase 4^2 times - that is 16 times.
Therefore option c) of the multiple choice is correct.
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