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The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by: [1] =, where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.
An algebraic rearrangement of this equation allows us to solve for rotational frequency: = / = /. Thus, the tangential speed will be directly proportional to r {\displaystyle r} when all parts of a system simultaneously have the same ω {\displaystyle \omega } , as for a wheel, disk, or rigid wand.
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 ...
Frequency dispersion of surface gravity waves on deep water. The red square moves with the phase velocity, and the green dots propagate with the group velocity. In this deep-water case, the phase velocity is twice the group velocity. The red square traverses the figure in the time it takes the green dot to traverse half.
The meaning of the constants and can be easily found: setting = on the equation above we see that () =, so that is the initial position of the particle, =; taking the derivative of that equation and evaluating at zero we get that ˙ =, so that is the initial speed of the particle divided by the angular frequency, =.
The graphs are two dimensional graphs. All the graphs are related by the equation “flow = speed * density”; this equation is the essential equation in traffic flow. The fundamental diagrams were derived by the plotting of field data points and giving these data points a best fit curve.
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
In many engineering applications the local flow velocity vector field is not known in every point and the only accessible velocity is the bulk velocity or average flow velocity ¯ (with the usual dimension of length per time), defined as the quotient between the volume flow rate ˙ (with dimension of cubed length per time) and the cross sectional area (with dimension of square length):