Understanding particular movement

[Susanne217]

Homework Statement

If the time of a particles movement at a certain position can be described

$$t_k = t_{k-1} + \Delta t$$

write an expression for the velocity at $$t_k$$


2. The attempt at a solution

if I assume that the corresponding position of the particle is

$$s_k = s_{k-1} + \Delta s$$

then it follows

that $$\frac{s_k}{t_k} = \frac{t_{k-1} + \Delta t}{s_{k-1} + \Delta s} = \frac{t_{k-1}}{s_{k-1}} + \frac{\Delta s}{\Delta t}$$

where $$\frac{s_{k}-s_{k-1}}{t_{k}-t_{k-1}} = \frac{\Delta s}{\Delta t} = v(t_i)$$

Can I assume this? No information about s is given. I am just using theory from my textbook..

 

[anathema]

it is important to always base our assumptions and conclusions on evidence and data. In this case, without any information about the position of the particle, we cannot make any assumptions about its velocity. It is important to gather data and perform experiments in order to accurately determine the velocity of the particle at a specific time. Additionally, the equation provided in the post only describes the relationship between time and position, not velocity. Therefore, it is not appropriate to assume the expression for velocity based on this equation alone. We must gather more information and use appropriate mathematical models to accurately determine the velocity of the particle.