+12 In my derivation for the tangential normal expression for an acceleration vector, I got that acceleration equals:
\(\vec{a}(t) = |\vec{v}|' \cdot \hat{T} + |\vec{v}| \cdot \hat{T}' \)
However, I also learned it can be expressed as:
\(\vec{a} = |\vec{v}\,'| \cdot \hat{T} + \kappa |\vec{v}|^2 \cdot \hat{N} \)
How are these two expressions the same? I especially don't understand how \(\kappa |\vec{v}|^2 \cdot \hat{N}\) is equal to \( |\vec{v}| \cdot \hat{T}'\)?
Someone please explain this, thanks in advance
