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| <h2>Solutions of Savchenko Problems in Physics</h2> | | <h2>Solutions of Savchenko Problems in Physics</h2> |
| <p class="author"> | | <p class="author"> |
| Aliaksandr Melnichenka <br/> | | Aliaksandr Melnichenka <br/> |
| October 2023 | | October 2023 |
| </p> | | </p> |
| </header> | | </header> |
| | | |
| <h3 id="back-link"><a href="../../#1.1">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.1">$\leftarrow$Back</a></h3> |
| | | |
| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $1.1.15.$ Using the velocity-time graphs, plot the coordinate-time graphs. In cases b and c find the average velocity over a large time. | | $1.1.15.$ Using the velocity-time graphs, plot the coordinate-time graphs. In cases b and c find the average velocity over a large time. |
| | | |
| </p> | | </p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" width="350" /> | | loading="lazy" width="350" /> |
| <figcaption> | | <figcaption> |
| For problem 1.1.15 | | For problem 1.1.15 |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| </p> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img id="sol" src="sol.png" | | <img id="sol" src="sol.png" |
| loading="lazy" alt="1.1.15" width="400" /> | | loading="lazy" alt="1.1.15" width="400" /> |
| <figcaption> | | <figcaption> |
| Graph-a of time dependence of coordinate | | Graph-a of time dependence of coordinate |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <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 the coordinate on 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 the coordinate on time. |
| </p> | | </p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="graph1.png" | | <img src="graph1.png" |
| loading="lazy" alt="1.1.15" width="400" /> | | loading="lazy" alt="1.1.15" width="400" /> |
| <figcaption> | | <figcaption> |
| Graph-b of time velocity of time | | Graph-b of time velocity of time |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| In case b), in equal time intervals, the body travels forward and backward the same distance. Consequently, for a large time, the displacement will be close to zero and the average velocity will be zero. | | In case b), in equal time intervals, the body travels forward and backward the same distance. Consequently, for a large time, the displacement will be close to zero and the average velocity will be zero. |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $v_{av} = 0 \; \text{m/s}$ | | $v_{av} = 0 \; \text{m/s}$ |
| </p> | | </p> |
| <br> | | <br> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="graph2.png" | | <img src="graph2.png" |
| loading="lazy" alt="1.1.15" width="400" /> | | loading="lazy" alt="1.1.15" width="400" /> |
| <figcaption> | | <figcaption> |
| Graph-c of time velocity of time | | Graph-c of time velocity of time |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| In case c) for equal time intervals, the body is no longer travelling equal distances. For every 4 seconds, it moves in the positive direction by 4 meters. | | In case c) for equal time intervals, the body is no longer travelling equal distances. For every 4 seconds, it moves in the positive direction by 4 meters. |
| </p> | | </p> |
| <p> | | <p> |
| Here we go: | | Here we go: |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $v_{av} = 1 \; \text{m/s}$ | | $v_{av} = 1 \; \text{m/s}$ |
| </p> | | </p> |
| </p> | | </p> |
| | | |
| <h4>Answer</h4> | | <h4>Answer</h4> |
| <p> | | <p> |
| <a href="#sol">See figure</a>; б) $v_{av} = 0$, в) $v_{av} = 1 \, \text{m/s}$ | | <a href="#sol">See figure</a>; б) $v_{av} = 0$, в) $v_{av} = 1 \, \text{m/s}$ |
| </p> | | </p> |
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