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Calculate the decrease in kinetic energy of a moving body if its velocity reduces to half of the initial velocity.

Last updated date: 17th Jun 2024
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Hint: To find the change in kinetic energy , we need to find the kinetic energy for given two situations separately. The kinetic energy of a moving object is related to its mass and velocity by the formula
${\text{K}}{\text{.E = }}\dfrac{1}{2}m{v^2}$

Complete step by step solution:
We know for kinetic energy, body must have velocity
Let initial velocity = v
& {\text{Also Kinetic energy is equal to}} \cr
& {\text{K}}{\text{.E}}{\text{. = }}\dfrac{1}{2}m{v^2} \cr
& {\text{given velocity decreased to half , so new velocity v'}} \cr
& {\text{v' = }}\dfrac{v}{2} \cr
& \Rightarrow {\text{K}}{\text{.}}{{\text{E}}_{new}} = {\text{ }}\dfrac{1}{2}m \times {\text{ (}}\dfrac{v}{2}{{\text{)}}^2} \cr
& \Rightarrow {\text{K}}{\text{.}}{{\text{E}}_{new}}{\text{ = }}\dfrac{1}{2}m\dfrac{{{v^2}}}{4} \cr
& \therefore {\text{K}}{\text{.}}{{\text{E}}_{new}}{\text{ = }}\dfrac{{m{v^2}}}{8} \cr
& {\text{Now as asked we need to find the decrease}} \cr
& \Delta {\text{K}}{\text{.E = }}\dfrac{{m{v^2}}}{2}{\text{ - }}\dfrac{{m{v^2}}}{8}{\text{ }} \cr
& \therefore \Delta {\text{K}}{\text{.E = }}\dfrac{3}{4}m{v^2} \cr
& {\text{Kinetic energy will decrease by }}\dfrac{3}{4}th{\text{ of initial kinetic energy}} \cr} $.

Additional information: Although the concept of kinetic energy dates back to the days of Aristotle, Lord Kelvin is first credited with using the term around 1849. Kinetic energy, the form of energy that is caused by the motion of an object or particle. If work, which transfers energy, is done by applying a net force on an object, the object moves and from which kinetic energy is obtained. The kinetic energy is the property of a moving object or particle also depends not only on the speed but also on the mass. The type of movement can be translation (or movement along a path from one place to another), moving around a spindle, vibration or any combination of movements.
There are two main types of kinetic energy: translational and rotational. The translational kinetic energy depends on the motion through space, and the rotational kinetic energy depends on the motion centered on the axis.

Note: The kinetic energy for any moving object can be calculated as long as the mass and speed of the objects are known. The unit used to measure kinetic energy is called Joule. If there are units of kilograms in mass and speed of meters per second, then kinetic energy consists of units of square-kilograms-kilograms per second.