Change in Kinetic Energy with Momentum Problem and Solution

Kinetic energy is the energy stored in the body by virtue of its motion. We can also express kinetic energy in terms of momentum. Momentum is a physical quantity which can be expressed as product of mass and velocity. It is a vector quantity and has the direction similar to velocity. Momentum explains how the given body can transfer kinetic energy between the two bodies during the interaction or collision.

Mass of a body is fundamental quantity and it is independent of any other physical quantities. As mass is constant, kinetic energy is directly proportional to square of the momentum.

Let us consider a scenario where kinetic energy of a given body is increased by 21% and we would like to know the corresponding change in momentum. The total kinetic energy of the body will be original kinetic energy and that additional kinetic energy. We can substitute this value in momentum relation and further simplified as shown below in the video.

By simplifying the mathematical equation it can be shown as the momentum increases by 10%.