<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
−
<meta name="description" content="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
−
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
−
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
−
papers.">
+
<meta name="description" content="A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.">
<meta property="og:title" content="A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.">
<meta property="og:image" content="img/logo.png">
−
<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
+
<meta property="og:description" content="A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.">
<title>A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.</title>
$1.1.16.$ A particle moves in one plane. From the graphs of the time dependence of the velocity projections $v_x$ and $v_y$ plot the trajectory of the particle if $x_{(0)} = 2$ m, $y_{(0)} = 1$ m.
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="320" />
<figcaption>
For problem 1.1.16
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
<p>
Taking into account the physical meaning of the area under the graph of velocity versus time, we obtain the graphs of the dependence of coordinate versus time.
</p>
<center>
<br>
<figure>
<img src="graph1.png"
loading="lazy" alt="1.1.16" width="350" />
<figcaption>
Graph of dependence $x(t)$
</figcaption>
</figure>
</center>
<br>
<center>
<figure>
<img src="graph2.png"
loading="lazy" alt="1.1.16" width="350" />
<figcaption>
Graph of dependence $y(t)$
</figcaption>
</figure>
</center>
<p>
Overlaying the graph of the dependence of $x(t)$ and $y(t)$ on each other at the corresponding time intervals, we obtain:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.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="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
<meta name="description" content="A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.">
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
<meta property="og:title" content="A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.">
<meta property="og:image" content="img/logo.png">
<meta property="og:image" content="img/logo.png">
<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
<meta property="og:description" content="A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.">
<title>A particle moves in one plane. From the graphs of the time dependence of the velocity projections v_x and v_y plot the trajectory of the particle if x_{(0)} = 2 m, y_{(0)} = 1 m.</title>
$1.1.16.$ A particle moves in one plane. From the graphs of the time dependence of the velocity projections $v_x$ and $v_y$ plot the trajectory of the particle if $x_{(0)} = 2$ m, $y_{(0)} = 1$ m.
$1.1.16.$ A particle moves in one plane. From the graphs of the time dependence of the velocity projections $v_x$ and $v_y$ plot the trajectory of the particle if $x_{(0)} = 2$ m, $y_{(0)} = 1$ m.
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="320" />
loading="lazy" width="320" />
<figcaption>
<figcaption>
For problem 1.1.16
For problem 1.1.16
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>
<p>
Taking into account the physical meaning of the area under the graph of velocity versus time, we obtain the graphs of the dependence of coordinate versus time.
Taking into account the physical meaning of the area under the graph of velocity versus time, we obtain the graphs of the dependence of coordinate versus time.
</p>
</p>
<center>
<center>
<br>
<br>
<figure>
<figure>
<img src="graph1.png"
<img src="graph1.png"
loading="lazy" alt="1.1.16" width="350" />
loading="lazy" alt="1.1.16" width="350" />
<figcaption>
<figcaption>
Graph of dependence $x(t)$
Graph of dependence $x(t)$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<br>
<br>
<center>
<center>
<figure>
<figure>
<img src="graph2.png"
<img src="graph2.png"
loading="lazy" alt="1.1.16" width="350" />
loading="lazy" alt="1.1.16" width="350" />
<figcaption>
<figcaption>
Graph of dependence $y(t)$
Graph of dependence $y(t)$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
Overlaying the graph of the dependence of $x(t)$ and $y(t)$ on each other at the corresponding time intervals, we obtain:
Overlaying the graph of the dependence of $x(t)$ and $y(t)$ on each other at the corresponding time intervals, we obtain:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
