- #1
Leo Liu
- 353
- 156
- Homework Statement
- Conceptual question
- Relevant Equations
- .
We know that in 1D, we can perform the following steps to obtain velocity in terms of time if the velocity is a function of position:
$$v=f(x)$$
$$dt=\frac{dx}{v}$$
$$t_2-t_1=\int_{x_1}^{x_2}\frac{dx}{v}$$
$$x(t)\rightarrow v(t)$$
But I wonder if it is possible to obtain ##\vec v(t)## from ##\vec v(\vec r)##? Does it even make sense to do something like $$\Delta t=\int_{r_{xi}}^{r_{xf}} \frac{d r_{x}}{v(r_x,r_y,r_z)}$$?
$$v=f(x)$$
$$dt=\frac{dx}{v}$$
$$t_2-t_1=\int_{x_1}^{x_2}\frac{dx}{v}$$
$$x(t)\rightarrow v(t)$$
But I wonder if it is possible to obtain ##\vec v(t)## from ##\vec v(\vec r)##? Does it even make sense to do something like $$\Delta t=\int_{r_{xi}}^{r_{xf}} \frac{d r_{x}}{v(r_x,r_y,r_z)}$$?
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