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.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.1.16.$ 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.

    <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:
        </p>
  <center>
    <figure>
      <img id="sol" src="sol.png"
        loading="lazy" alt="1.1.16" width="200" />
    <figcaption>
      Trajectory of movement
    </figcaption>
    </figure>
  </center>

    </p>

    <h4>Answer</h4>
    <p>
        <a href="#sol">See figure</a>.
    </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>