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+ <h2>Solutions of Savchenko Problems in Physics</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../#1.2">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.2.5.$ When entering a damaged section of the highway, each car in a convoy reduces its speed from $v_1$ to $v_2$. What should be the distance between the cars so that they do not collide? The length of each car is $l$.
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <p>
+Let's move to the frame of reference associated with the $1$th car at the moment when it enters the damaged area and starts moving with velocity $v_2$. The second car will move with a velocity equal to the velocity difference
+$$v_\text{from}=v_1-v_2$$
+</p>
+<p>
+Время, которое проедет второй автомобиль, в системе отсчета «остановленного» первого автомобиля равно
+</p>
+<p>
+<center>$$t=\frac{L}{v_1–v_2},\, (1)$$</center>
+</p>
+<p>
+где $L$ - дистанция между автомобилями.
+</p>
+<p>
+За время $t$ первый автомобиль с измененной скоростью $v_2$ должен проехать минимум расстояние равное длине автомобиля
+</p>
+<p>
+<center>$$t=\frac{l}{v_2} \, (2)$$</center>
+</p>
+<p>
+Приравняем $(1)$ и $(2)$
+</p>
+<p>
+<center>$$\frac{L}{v_1–v_2}=\frac{l}{v_2}$$</center>
+</p>
+<p>
+Откуда искомая дистанция между автомобилями, при которой они еще не столкнутся равна
+</p>
+<p>
+<center>$$\fbox{$L \geq \frac{v_1–v_2}{v_2} \cdot l$}$$</center>
+</p>
+
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$L=\frac{v_1–v_2}{v_2} \cdot l$$
+ </p>
+
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