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F is the resultant force applied, t 1 and t 2 are times when the impulse begins and ends, respectively, m is the mass of the object, v 2 is the final velocity of the object at the end of the time interval, and; v 1 is the initial velocity of the object when the time interval begins. Impulse has the same units and dimensions (MLT −1) as momentum.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
A set of equations describing the trajectories of objects subject to a constant gravitational force under normal Earth-bound conditions.Assuming constant acceleration g due to Earth's gravity, Newton's law of universal gravitation simplifies to F = mg, where F is the force exerted on a mass m by the Earth's gravitational field of strength g.
A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force. At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time.
Assuming that the masses are constant, G is one-half the time derivative of this moment of inertia: = = = = = = =. In turn, the time derivative of G is = = + = = = + = = + =, where m k is the mass of the k th particle, F k = dp k / dt is the net force on that particle, and T is the total kinetic energy of the system according to the v k ...
Equation [3] involves the average velocity v + v 0 / 2 . Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows ...
This is the "textbook" case of the vertical motion of an object falling a small distance close to the surface of a planet. It is a good approximation in air as long as the force of gravity on the object is much greater than the force of air resistance, or equivalently the object's velocity is always much less than the terminal velocity (see below).
This is an approximation: the actual random force has a nonzero correlation time corresponding to the collision time of the molecules. However, the Langevin equation is used to describe the motion of a "macroscopic" particle at a much longer time scale, and in this limit the δ {\displaystyle \delta } -correlation and the Langevin equation ...