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Simple difference between module of velocity and time derivative of module of position [duplicate]
What is the conceptually difference between the two:
$$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ ...
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1/velocity for higher dimensions
I have a somewhat basic question. I am sorry if it trivial.
Denote the velocity by $v=\frac{dx}{dt}$ suppose that $x \in \mathbb{R}^n$ and I want to parametrize $t$ in $x$ and compute $\frac{dt}{dx}$. ...
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Suppose there is a vector $\vec v$ which is a function of time, then will $\dfrac{d}{dt}|\vec v|$ be a vector quantity or a scalar quantity?
Suppose there is a vector $\vec v$ which is a function of time, then will $\dfrac{d}{dt}|\vec v|$ be a vector quantity or a scalar quantity?
I think it should be scalar because, let's assume $\vec v=...
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