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| <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> | | <span><img src="../../img/book.png"></span><span>Savchenko Solutions</span> |
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| <p class="author"> | | <p class="author"> |
| Solutions of Savchenko Problems in Physics <br> | | Solutions of Savchenko Problems in Physics <br> |
| <i><b>knowledge must be free</b></i> | | <i><b>knowledge must be free</b></i> |
| </p> | | </p> |
| </header> | | </header> |
| | | |
| <h3 id="back-link"><a href="../../#1.2">$\leftarrow$Back</a></h3> | | <h3 id="back-link"><a href="../../#1.2">$\leftarrow$Back</a></h3> |
| | | |
| <h3> Statement </h3> | | <h3> Statement </h3> |
| <p> | | <p> |
| $1.2.2.$ Two particles at time $t = 0$ have left the same point. Using the velocity-time graphs, determine the coordinates and time of the new meeting of the particles. | | $1.2.2.$ Two particles at time $t = 0$ have left the same point. Using the velocity-time graphs, determine the coordinates and time of the new meeting of the particles. |
| </p> | | </p> |
| <center> | | <center> |
| <figure> | | <figure> |
| <img src="statement.png" | | <img src="statement.png" |
| loading="lazy" width="230" /> | | loading="lazy" width="230" /> |
| <figcaption> | | <figcaption> |
| For problem $1.2.2$ | | For problem $1.2.2$ |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| <p> | | <p> |
| </p> | | </p> |
| | | |
| <h3>Solution</h3> | | <h3>Solution</h3> |
| <p> | | <p> |
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| <figure> | | <figure> |
| <img src="Plot.png" alt="1.2.2" | | <img src="Plot.png" alt="1.2.2" |
| loading="lazy" width="350" /> | | loading="lazy" width="350" /> |
| <figcaption> | | <figcaption> |
| Coordinates of points and their intersection | | Coordinates of points and their intersection |
| </figcaption> | | </figcaption> |
| </figure> | | </figure> |
| </center> | | </center> |
| | | |
| <p> | | <p> |
| 1. Equations of motion of particles. | | 1. Equations of motion of particles. |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $$ | | $$ |
| {x_{1}(t) = v_{1}t, \quad x_{2}(t) = \frac{at^2}{2}} | | {x_{1}(t) = v_{1}t, \quad x_{2}(t) = \frac{at^2}{2}} |
| $$ | | $$ |
| </p> | | </p> |
| <p> | | <p> |
| 2. The velocity of the first particle and acceleration of the second particle are determined by the given dependence $v = f(t)$: | | 2. The velocity of the first particle and acceleration of the second particle are determined by the given dependence $v = f(t)$: |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $$ | | $$ |
| {v_{1} = 2\; \frac{m}{s}}, \quad a \equiv 0.33\; \frac{m}{s^{2}}. | | {v_{1} = 2\; \frac{m}{s}}, \quad a \equiv 0.33\; \frac{m}{s^{2}}. |
| $$ | | $$ |
| </p> | | </p> |
| <p> | | <p> |
| 3. Particle encounter condition: | | 3. Particle encounter condition: |
| </p> | | </p> |
| <p style="text-align: center;"> | | <p style="text-align: center;"> |
| $$ | | $$ |
| x_{1}(t_{z}) = x_{2}(t_{z}). \quad t_{z} = \frac{2v_{z}}{a} = 12\; c, \quad x_{z} = 24\; m. | | x_{1}(t_{z}) = x_{2}(t_{z}). \quad t_{z} = \frac{2v_{z}}{a} = 12\; c, \quad x_{z} = 24\; m. |
| $$ | | $$ |
| </p> | | </p> |
| </p> | | </p> |
