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+ <h2>Solutions of Savchenko Problems in Physics</h2>
+ <p class="author">
+ Aliaksandr Melnichenka <br/>
+ October 2023
+ </p>
+ </header>
+
+ <h3 id="back-link"><a href="../../#1.3">$\leftarrow$Back</a></h3>
+
+ <h3> Statement </h3>
+ <p>
+ $1.3.25.$ A small body moves along a circle of radius $r$ at a speed that increases linearly in time according to the law $v = kt$. Find the dependence of the total acceleration of the body on time.
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+ <p>We will decompose the acceleration into two components, tangential $a_\parallel $ and normal $a_\perp$</p>
+<p>In the longitudinal direction, the acceleration $a_\parallel $ is associated with the change in speed </p>
+<p class="exp">
+$$a_\parallel = k$$
+</p>
+<p>In the transverse direction, the acceleration $a_\perp $ is a consequence of the centrifugal force</p>
+<p class="exp">
+$$ a_\perp = \frac{v^2}{r} = \frac{k^2t^2}{r} $$
+</p>
+<p>Full acceleration</p>
+<p class="exp">
+$$a = \sqrt{a^2_\perp + a^2_\parallel}$$
+</p>
+<p>Substitute the obtained components</p>
+<p class="exp">
+$$ \boxed{a = \sqrt{\frac{k^4t^4}{r^2} + k^2}} $$
+</p>
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$a = \sqrt{\frac{k^4t^4}{r^2} + k^2}$$
+ </p>
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