<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="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.">
<meta property="og:title" content="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.">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="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.">
<title>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.</title>
$1.2.5.$ 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
<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>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
<meta name="description" content="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.">
<meta name="description" content="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.">
<meta property="og:title" content="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.">
<meta property="og:title" content="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.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
@@ -14,9 +14,9 @@
<meta property="og:description" content="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.">
<meta property="og:description" content="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.">
<title>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.</title>
<title>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.</title>
$1.2.5.$ 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 $l$.
$1.2.5.$ 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>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<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
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
$$v_\text{from}=v_1-v_2$$
$$v_\text{from}=v_1-v_2$$
</p>
</p>
<p>
<p>
Время, которое проедет второй автомобиль, в системе отсчета «остановленного» первого автомобиля равно
Время, которое проедет второй автомобиль, в системе отсчета «остановленного» первого автомобиля равно
</p>
</p>
<p>
<p>
<center>$$t=\frac{L}{v_1–v_2},\, (1)$$</center>
<center>$$t=\frac{L}{v_1–v_2},\, (1)$$</center>
</p>
</p>
<p>
<p>
где $L$ - дистанция между автомобилями.
где $L$ - дистанция между автомобилями.
</p>
</p>
<p>
<p>
За время $t$ первый автомобиль с измененной скоростью $v_2$ должен проехать минимум расстояние равное длине автомобиля
За время $t$ первый автомобиль с измененной скоростью $v_2$ должен проехать минимум расстояние равное длине автомобиля
<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>
<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>
