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The worldlines of W 1 and W′ 1 are the corresponding vertical time axes (ct in the upper pictures, and ct′ in the lower pictures). In the upper picture the place for W 2 is taken to be A x > 0, and thus the worldline (not shown in the pictures) of this clock intersects the worldline of the moving clock (the ct ′-axis) in the event ...
Instead, the relative velocity β = v / c between and ′ can directly be used in the following construction, providing the same result: [15] If φ is the angle between the axes of ct′ and ct (or between x and x′), and θ between the axes of x′ and ct′, it is given: [15] [16] [17] [18]
The four-velocity at any point of world line () is defined as: = where is the four-position and is the proper time. [1] The four-velocity defined here using the proper time of an object does not exist for world lines for massless objects such as photons travelling at the speed of light; nor is it defined for tachyonic world lines, where the ...
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
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.
While 70% of boomers have zero tolerance for any level of tardiness, in Gen Z’s eyes, 10 minutes late is still on time—explaining the friction between the two generations at work. (hobo_018 ...
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.)