Question

How do we find velocity from position (or distance) if they are both vectors in physics?

Answer 1

In physics, if you have information about the position or distance of an object and you want to determine its velocity, you need to consider the concept of differentiation. Differentiation allows you to find the derivative of a position function with respect to time, which gives you the velocity.

To find the velocity from position, you would typically use calculus and differentiate the position function with respect to time. The position function describes how the position of the object changes over time.

If you have a position function $x(t)$, where $x$ represents the position and $t$ represents time, you can find the velocity function $v(t)$ by differentiating the position function with respect to time:

$v(t)=\frac{dx(t)}{dt}$

In vector form, if you have a position vector $\mathbf{r}(t)=\left(\begin{array}{c}x(t)\\ y(t)\\ z(t)\end{array}\right)$, where $x(t)$, $y(t)$, and $z(t)$ represent the components of the position vector in the x, y, and z directions respectively, you can find the velocity vector <mi mathvaria