Solución
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\begin{aligned} \|\bold{v}(t)\| &= k\\ \bold{v}(t)\cdot\bold{v}(t) &= k\\ \frac{d}{dt}(\bold{v}(t)\cdot\bold{v}(t)) &= \frac{d}{dt}k = 0\\ \bold{v}(t)\cdot\bold{v'}(t)+\bold{v'}(t)\cdot\bold{v}(t) &= 0\\ 2\bold{v}(t)\cdot\bold{v'}(t) &=0\\ \bold{v}(t)\cdot\bold{v'}(t) &=0 \end{aligned}
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La última afirmación implica que la velocidad y la aceleración son perpendiculares u ortogonales.