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Trajectory of a particle with initial position vector r 0 and velocity v 0, subject to constant acceleration a, all three quantities in any direction, and the position r(t) and velocity v(t) after time t. The initial position, initial velocity, and acceleration vectors need not be collinear, and the equations of motion take an almost identical ...
Unprimed quantities refer to position, velocity and acceleration in one frame F; primed quantities refer to position, velocity and acceleration in another frame F' moving at translational velocity V or angular velocity Ω relative to F. Conversely F moves at velocity (—V or —Ω) relative to F'. The situation is similar for relative ...
The drift velocity, and resulting current, is characterized by the mobility; for details, see electron mobility (for solids) or electrical mobility (for a more general discussion). See drift–diffusion equation for the way that the drift current, diffusion current , and carrier generation and recombination are combined into a single equation.
At low fields, the drift velocity v d is proportional to the electric field E, so mobility μ is constant. This value of μ is called the low-field mobility. As the electric field is increased, however, the carrier velocity increases sublinearly and asymptotically towards a maximum possible value, called the saturation velocity v sat.
Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on. A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing ...
Then, by taking time derivatives, formulas are derived that relate the velocity of the particle as seen in the two frames, and the acceleration relative to each frame. Using these accelerations, the fictitious forces are identified by comparing Newton's second law as formulated in the two different frames.
The current 3-form can be integrated over a 3-dimensional space-time region. The physical interpretation of this integral is the charge in that region if it is spacelike, or the amount of charge that flows through a surface in a certain amount of time if that region is a spacelike surface cross a timelike interval.
Blue line: drag force; red line: inertia force; black line: total force according to the Morison equation. Note that the inertia force is in front of the phase of the drag force: the flow velocity is a sine wave, while the local acceleration is a cosine wave as a function of time.