Short answers, pulled from the story.
Willem 's Gravesande made this discovery in 1722. He dropped weights into blocks of clay and found that the depth of the sink was proportional to the square of the speed rather than the speed itself. This experiment proved that the force of impact was tied to the square of the velocity.
Émilie du Châtelet translated Isaac Newton's Principia into French and published the first clear explanation of the relationship between mass speed and energy. Born in 1706 she was a brilliant mathematician and physicist who established that the energy of a moving object is equal to half the product of its mass and the square of its speed. Her work bridged the gap between the experimental data of Gravesande and the theoretical frameworks of the time.
William Thomson later known as Lord Kelvin coined the term kinetic energy around 1849. He worked alongside Peter Tait to replace the word actual with kinetic creating a pair of antithetical adjectives that would distinguish between energy of activity and energy of configuration. Thomas Young was the first to use the word energy to refer to kinetic energy in its modern sense during a lecture to the Royal Society in 1802.
When a cyclist reaches the top of a hill and comes to a complete halt that kinetic energy has been largely converted into gravitational potential energy. Friction and air resistance convert some of that energy into thermal energy which is why the cyclist never regains all of their speed without additional pedaling. This transformation illustrates the principle that energy is not destroyed but rather converted from one form to another.
In relativistic mechanics the kinetic energy is defined as the total energy minus the rest energy which is the energy an object possesses simply by virtue of having mass. As the speed of the object approaches the speed of light the energy required to accelerate it further increases exponentially making it impossible for any object with mass to reach the speed of light. The total energy of an object combines with its momentum in a way that is analogous to the combination of time and space into spacetime.
The internal kinetic energy of a macroscopic body that appears to be stationary is contributed by the motion of its constituent particles. In a tank of gas the molecules are moving in all directions and their collective motion contributes to the body's temperature and pressure. This internal kinetic energy is also present in the rotation and vibration of atoms and electrons as well as in the spin of nuclear particles.