Posted: Dec 26, 2019 3:52 pm
demarmat wrote:The object moves and at the same time (AT THE SAME TIME!!!) changes its speed (slows down or speeds up). My acceleration is not a vector and has no direction! Apparently Einstein also had the same opinion, but he couldn't explain it. I can! When d = 1, the object moves uniformly at the same speed. When d < 1, the object slows down, and when d > 1, the object speeds up. And when d = 0 then the object does not move at all. What is hard to understand here! Now I have a question: how did so many mindless trolls get into this forum?
Acceleration is a vector because not all motion is linear (e.g. a planet orbiting a sun, a car turning a corner). In equations of linear motion, which are restricted cases where the acceleration (or deceleration) and motion are all colinear acceleration is treated as a signed real, not a vector.
For example under uniform acceleration:
s = ut + 1/2 at2
If one further restricts the case, so that u=0 then one gets:
s = 1/2 at2
Which will give
a = 2s/t2, unlike your OP, which implies the correct formula is a = d/t2 (which I think is just some sort of error resulting from dropping of deltas and/or small value approximations in equations). As has been said dimensional analysis of the quantities in your OP shows the units are inconsistent and indicate an error as well, when you assume n=d in general cases of acceleration.
You can also see that easily in simple examples involving your equation a = d2/t. An object dropped from 45m under Earth's freefall gravitic acceleration (~10m/s2) does indeed take ~3sec to fall to Earth, as it should, not as it would under your suggestion (I'd calculate that, but of course there is no fixed value for g under your idea, so I can't).
There's probably no point going further, but even if one did the superficial similarity between equations like "a = d²/t [compared] to the Planck constant h = md²/t" is not a physical reason to justify anything.