Physics, 01.03.2021 15:20 natd299736
A particle move in the xy plane so that its position vector r=bcosQi +bsinQj+ ctk, where b, Q and c are constants. show that the partial move with constant speed.
Answers: 1
. 
:
.
as a column vector to distinguish between the components:
.
and 
are constants. Therefore, 
and 
would also be constants with respect to ![\displaystyle \frac{d}{dt}[b\, \cos(Q)] = 0](/tpl/images/1156/5689/5a47a.png)
and ![\displaystyle \frac{d}{dt}[b\, \sin(Q)] = 0](/tpl/images/1156/5689/544b6.png)
.
:![\begin{aligned}\mathbf{v}(t) &= \frac{\rm d}{{\rm d} t} [\mathbf{r}(t)] \\ &=\frac{\rm d}{{\rm d} t} \left(\begin{bmatrix}b\, \cos(Q) \\ b\, \sin(Q) \\ c\, t\end{bmatrix}\right) \\ &= \begin{bmatrix}\displaystyle \frac{d}{dt}[b\, \cos(Q)] \\[0.5em] \displaystyle \frac{d}{dt}[b\, \sin(Q)]\\[0.5em]\displaystyle \frac{d}{dt}[c \cdot t]\end{bmatrix} = \begin{bmatrix}0 \\ 0 \\ c\end{bmatrix}\end{aligned}](/tpl/images/1156/5689/63f4a.png)
.
(a scalar) of a particle is the magnitude of its velocity :
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