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Hritik Narayan
Hritik Narayan
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Actually, regardless of the velocity of the objects in concern, the 'velocity addition' formula is always $\frac{u+v}{1+uv/c^2}$.

There is no transition point where the formula changes from $u+v$ to the special relativity one. Its just that the difference you get in both the formulas at 'low velocities' is very very negligible. $c^2$, in $m/s$$m^2/s^2$, is $9*10^{16}$. The average speed of a bus is $3.6$ $m/s$. Even for much larger $u,v$ values than that, $uv/c^2$ is negligible. This is why the formula is not of much use in low velocity cases. The significance is observed when $uv/c^2$ is a significant portion of $1$.

Actually, regardless of the velocity of the objects in concern, the 'velocity addition' formula is always $\frac{u+v}{1+uv/c^2}$.

There is no transition point where the formula changes from $u+v$ to the special relativity one. Its just that the difference you get in both the formulas at 'low velocities' is very very negligible. $c^2$, in $m/s$, is $9*10^{16}$. The average speed of a bus is $3.6$ $m/s$. Even for much larger $u,v$ values than that, $uv/c^2$ is negligible. This is why the formula is not of much use in low velocity cases. The significance is observed when $uv/c^2$ is a significant portion of $1$.

Actually, regardless of the velocity of the objects in concern, the 'velocity addition' formula is always $\frac{u+v}{1+uv/c^2}$.

There is no transition point where the formula changes from $u+v$ to the special relativity one. Its just that the difference you get in both the formulas at 'low velocities' is very very negligible. $c^2$, in $m^2/s^2$, is $9*10^{16}$. The average speed of a bus is $3.6$ $m/s$. Even for much larger $u,v$ values than that, $uv/c^2$ is negligible. This is why the formula is not of much use in low velocity cases. The significance is observed when $uv/c^2$ is a significant portion of $1$.

Source Link
Hritik Narayan
Hritik Narayan
  • 7.5k
  • 3
  • 34
  • 46

Actually, regardless of the velocity of the objects in concern, the 'velocity addition' formula is always $\frac{u+v}{1+uv/c^2}$.

There is no transition point where the formula changes from $u+v$ to the special relativity one. Its just that the difference you get in both the formulas at 'low velocities' is very very negligible. $c^2$, in $m/s$, is $9*10^{16}$. The average speed of a bus is $3.6$ $m/s$. Even for much larger $u,v$ values than that, $uv/c^2$ is negligible. This is why the formula is not of much use in low velocity cases. The significance is observed when $uv/c^2$ is a significant portion of $1$.