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It is the first time-integral of the displacement [3] [4] (i.e. absement is the area under a displacement vs. time graph), so the displacement is the rate of change (first time-derivative) of the absement. The dimension of absement is length multiplied by time.
The Hubble length or Hubble distance is a unit of distance in cosmology, defined as cH −1 — the speed of light multiplied by the Hubble time. It is equivalent to 4,420 million parsecs or 14.4 billion light years.
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.)
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 from solving [1] for
Another method is to use a clock indicating its proper time, which is traveling from one endpoint of the rod to the other in time as measured by clocks in the rod's rest frame. The length of the rod can be computed by multiplying its travel time by its velocity, thus L 0 = T ⋅ v {\displaystyle L_{0}=T\cdot v} in the rod's rest frame or L = T ...
For convenience, consider contact with the spring occurs at t = 0, then the integral of the product of the distance x and the x-velocity, xv x dt, over time t is 1 / 2 x 2. The work is the product of the distance times the spring force, which is also dependent on distance; hence the x 2 result.
() is the time interval. is the scalar distance for the second observation of ... (which is the slant distance multiplied by the slant direction vector): ...
When velocity is constant, the total distance traveled over the given time interval can be computed by multiplying velocity and time. For example, travelling a steady 50 mph for 3 hours results in a total distance of 150 miles.