February 07, 2025
On a number line, there are infinitely many points between any two nearest numbers. When you say "1," you are actually referring to the difference between 0 and 1, with an infinite sequence of points in between.
Similarly, while the speed of light (c) appears constant on large scales, at an infinitesimally small scale, it has a beginning due to transmission delay. This delay occurs because motion progresses incrementally, however small, starting from absolute rest (v=0) before reaching c.
The first phase, where velocity increases from 0 to c, represents acceleration. Motion does not begin with an arbitrary velocity but transitions from rest. The first phase starts at zero (v = 0) and progresses to an initial velocity (v), whereas successive phases continue from an already established velocity (v = v) rather than starting anew v = 0.
The idea is mathematically presented here:
Let v(t) represent the velocity of the object as a function of time. In the first phase of motion:
Initial Phase (Acceleration):
The motion begins from rest, so at t = 0, v(0) = 0. The velocity increases from v = 0 to some initial velocity v₁ = c, over some time interval Δt₁. The acceleration a(t) in this phase is given by:
a(t) = dv(t)/dt, where v(t) =∫a(t)dt
The velocity increases gradually from 0 to c, so during this phase, the object undergoes acceleration.
Subsequent Phases (Constant Velocity):
After reaching an initial velocity v₁ = c, successive phases of motion proceed at this established velocity. In these phases, the velocity remains constant, so for t > Δt₁, we have: v(t) = v₁ = c, a(t) = 0
In the subsequent phases, the object continues with the velocity v = c, without starting from rest or accelerating further.
No comments:
Post a Comment