The scheduled departure time of the train is 12.00. It's 12.00 on your watch, but the penultimate car that moves past you during time t_1 is already starting to pass by you.The last car passes you during t_2. The train left on time and is moving equidistant. How far behind is your watch?

Savchenko Solutions

Solutions of Savchenko Problems in Physics
knowledge must be free

    <h3 id="back-link"><a href="/#1.2">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.2.21^*.$ The scheduled departure time of the train is $12.00$. It's $12.00$ on your watch, but the penultimate car that moves past you during time $t_1$ is already starting to pass by you.

The last car passes you during $t_2$. The train left on time and is moving equidistant. How far behind is your watch?

    <h3>Solution</h3>
    <p>
        $$l=\nu _{1}t_{1} +\frac{at_{1}^{2}}{2}$$

$$l=(\nu _{1}+at_{1})t_{2} +\frac{at_{1}^{2}}{2}$$

$$(\nu _{1}+at_{1})t_{2} +\frac{at_{1}^{2}}{2} = \nu _{1}t_{1} +\frac{at_{1}^{2}}{2}$$
Given that $\nu _{1} = a{d}t$:
$$a{d}t(t_{1}-t_{2}) =\frac{a(t_{2}-2t_{1}t_{2}-t_{1}^{2})}{2}$$
$${d}t=\fbox{$\frac{t_{2}-2t_{1}t_{2}-t_{1}^{2}}{2(t_{1}-t_{2})}$}$$

Dzikan Danila

    </p>

    <h4>Answer</h4>
    <p>
        $$\frac{t_{2}-2t_{1}t_{2}-t_{1}^{2}}{2(t_{1}-t_{2})}$$
    </p>


<footer class="row container">
  <br>
    <p>
        <small> © <strong>Savchenko Solutions</strong>, 2023-2024 <br></small>
    </p>
    <p>
        <small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> alex@savchenkosolutions.com <br></small>
    </p>
</footer>