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The derivation of the work–energy principle begins with Newton's second law of motion and the resultant force on a particle. Computation of the scalar product of the force with the velocity of the particle evaluates the instantaneous power added to the system. [27] (Constraints define the direction of movement of the particle by ensuring ...
In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. [ 1 ] In classical mechanics , the kinetic energy of a non-rotating object of mass m traveling at a speed v is 1 2 m v 2 {\textstyle {\frac {1}{2}}mv^{2}} .
For example, in 1742, Émilie du Châtelet wrote, "Dead force consists of a simple tendency to motion: such is that of a spring ready to relax; living force is that which a body has when it is in actual motion." In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. [136]
Power is the rate with respect to time at which work is done; it is the time derivative of work: =, where P is power, W is work, and t is time.. We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product: = =
It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time .
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
kinetic energy of the microscopic motion of particles, ... a function of energy, is force times distance. = ... In classical physics, energy is a scalar quantity, ...
In physics, the energy–momentum relation, or relativistic dispersion relation, is the relativistic equation relating total energy (which is also called relativistic energy) to invariant mass (which is also called rest mass) and momentum. It is the extension of mass–energy equivalence for bodies or systems with non-zero momentum.