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In SI, this slope or derivative is expressed in the units of meters per second per second (/, usually termed "meters per second-squared"). 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 ...
In terms of a displacement-time (x vs. t) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the slope of the tangent line to the curve at any point, and the average velocity as the slope of the secant line between two points with t coordinates equal to the boundaries of the time period for the average velocity.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
The slope of the world line (deviation from being vertical) is the velocity of the particle on that section of the world line. Bends in the world line represent particle acceleration. As the particle accelerates, its view of spacetime changes. These changes in view are governed by the Lorentz transformations. Also note that:
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 ...
Hubble's law can be easily depicted in a "Hubble diagram" in which the velocity (assumed approximately proportional to the redshift) of an object is plotted with respect to its distance from the observer. [30] A straight line of positive slope on this diagram is the visual depiction of Hubble's law.
V is velocity (in ft/s for US customary units, in m/s for SI units) k is a conversion factor for the unit system (k = 1.318 for US customary units, k = 0.849 for SI units) C is a roughness coefficient; R is the hydraulic radius (in ft for US customary units, in m for SI units) S is the slope of the energy line (head loss per length of pipe or h ...
Roughness length is a parameter of some vertical wind profile equations that model the horizontal mean wind speed near the ground. In the log wind profile , it is equivalent to the height at which the wind speed theoretically becomes zero in the absence of wind-slowing obstacles and under neutral conditions.