Suppose a body is moving with a constant speed of $10~\mathrm{ms^{-1}}$ in negative $x$ direction in $x$-$y$ plane. Let $\vec r$ be the position vector.
Then what will be the instantaneous velocity vector?
I know it will be $-10\hat{i}$, but how do I calculate that using this:
$$\vec{v} = \dfrac{d\vec{r}}{dt}.$$
Best Answer
You first write your position vector as $\vec r = (x_0 -t\cdot10~\mathrm{m/s},y_0)$ and then take the derivative of that.
This produces $$\vec v = \frac{d\vec r}{dt}=(-10,0)~\mathrm{ms^{-1}}=-10\hat i\,~\mathrm{ms^{-1}}$$ which is what you want.