In science, kinetic energy is the quantity of work:

that must be done to bring a body of mass m, initially at rest, to a velocity v. [1]

History
In 1689, German mathematician Gottfried Leibniz had defined the following quantity, determined previously to be conserved in perfectly elastic collistions in 1669 by Dutch physicist Christiaan Huygens, as vis viva or living force:

Vis viva = mv²

In 1807, English physicist Thomas Young defined the above quantity as "energy":

E = mv²

In 1811, Italian mathematician Joseph Lagrange used calculus to show that a factor of two is involved in the relationship “potential” (potential energy) and “vis viva” (kinetic energy). [2] As defined via the symbols used by Lagrange, i.e. T as kinetic energy, in his 1788 Analytical Mechanics, kinetic energy was thus defined as:

where 2T denotes the whole "living force of the system". [3]

See also
● Kinetic theory

References
1. Perrot, Pierre. (1998). A to Z of Thermodynamics, Oxford: Oxford University Press.
2. Rayner, John, N. (2000). Dynamic Climatology: Basis in Mathematical Physics, (pg. 94). Blackwell Publishing.
3. (a) Hamilton, W.R. (1834). “On a general method in dynamics by which the study of the motions of all free systems of attracting or repelling points is reduced to the search and differentiation of one central relation, or characteristic function.” Philos. Trans. R. Soc. London, 124:247-308.
(b) Hamilton, W.R. (1835). “A second essay on a general method in dynamics.” Philos. Trans. R. Soc. London, 125:95-144.