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+ <meta name="description" content="The particle, after leaving the source, flies at a constant speed for a distance L, and then decelerates with acceleration a. At what speed will the particle have the shortest travel time from its departure to its stop?">
+ <meta name="author" content="Aliaksandr Melnichenka">
+ <meta name="date" content="2023-10" scheme="YYYY-MM">
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+ <header style="text-align:center;">
+ <h2>Solutions of Savchenko Problems in Physics</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../#1.2">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.2.8^*.$ The particle, after leaving the source, flies at a constant speed for a distance $L$, and then decelerates with acceleration $a$. At what speed will the particle have the shortest travel time from its departure to its stop?
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <p>
+On a constant velocity interval, the velocity is:
+</p>
+<p style="text-align: center;">
+$$v_0 = \frac{L}{t}$$
+</p>
+<p>
+During the deceleration interval the velocity changes as
+</p>
+<p style="text-align: center;">
+$v(t) = v_0-at \Rightarrow v_0=at$
+</p>
+<p>
+Equating the equations, we obtain
+</p>
+<p style="text-align: center;">
+$L=at^2$
+</p>
+<p>
+From where
+</p>
+<p style="text-align: center;">
+$v_0 = \sqrt{La}$
+</p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$v = \sqrt{La}$$
+ </p>
+
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