What does $∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ a n d \frac{d | \to v |}{d t}$ represent?

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Solution

$\frac{d | \to v |}{d t}$ represents rate of change of speed of the particle whereas $∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣$ represents the magnitude of rate of change of its velocity (OR magnitude of acceleration).
For example : In case of uniform circular motion, $\frac{d | \to v |}{d t} = 0$ whereas $∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ \neq 0$

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Similar questions

\frac{d | \to v |}{d t} \neq 0 w h i l e ∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ = 0

\frac{d | \to v |}{d t} = 0 w h i l e ∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ \neq 0

X - Z

\to r = v_{0} t^i + a_{0} e^{b_{0} t}^k

(\begin{matrix} \to v = \frac{d \to r}{d t} \end{matrix})

(\begin{matrix} | \begin{matrix} \to v \end{matrix} | \end{matrix})

(\begin{matrix} \frac{d \to v}{d t} \end{matrix})

what does |dv/dt| and d|v|/dt represent . Can these be equal.

∣ ∣ ∣ \frac{d \to v}{d t} ∣ ∣ ∣ \neq 0

\frac{d}{d t} | \to v | = 0

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