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Suppose one person at $t_0$ is at the location $p_0$

at $t_1$ is at the location $p_1$

at $t_2$ is at the location $p_2$

Then question: this person velocity at $t_1$ is $(p_1-p_0)/(t_1-t_0)$ Or $(p_2-p_1)/(t_2-t_1)$ ? Which one has more physical meaning? suppose $(t_2-t_1)$ and $(t_1-t_0)$ is small.

Also, suppose we only have the above data. It seems we can only use $(p_1-p_0)/(t_1-t_0)$ at $t_0$, and $(p_2-p_1)/(t_2-t_1)$ at $t_2$. Is it ok to not use the same way to calculate the speed?

It seems at least there are two phases in which the person has the same velocity,(strange).

Thank you very much.

Update: if the three time is not very close, which way is better to approximate the speed.

ytyyutianyun
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1 Answers1

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If all three times are close together, then you would expect the velocity not to change very much between the points, since

$$∆v = a∆t \rightarrow 0$$

The equations you've given are only an approximation. Thus we expect

$$\frac{p_2-p_1}{t_2-t_1} \approx \frac{p_1-p_0}{t_1-t_0}$$

HiddenBabel
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