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+ <title>A body for time t_0 moves with constant velocity v_0. Then its velocity increases linearly with time so that at time 2 t_0 it is equal to 2 v_0. Determine the path traveled by the body for time t > t_0.</title>
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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>
+ $1.2.3.$ A body for time $t_0$ moves with constant velocity $v_0$. Then its velocity increases linearly with time so that at time $2 t_0$ it is equal to $2 v_0$. Determine the path traveled by the body for time $t > t_0$.
+</p>
+<center>
+ <figure>
+ <img src="statement.png"
+ loading="lazy" width="230" />
+ <figcaption>
+ For problem $1.2.3$
+ </figcaption>
+ </figure>
+</center>
+<p>
+ </p>
+
+ <h3>Solution</h3>
+ <p>
+
+<p>
+At time $t_0$, the coordinate was $x_1=v_0t_0$.
+</p>
+<p>
+On the interval from $t_0$ to $2t_0$, the acceleration is constant and equal to $a=\frac{v_0}{t_0}$.
+</p>
+<p>
+In the case of equiaxcelerated motion with initial velocity $v_0$ from time $t_0$, the path is found as
+</p>
+<p style="text-align: center;">
+$$
+x_2 = v_0 (t-t_0)+\frac{a(t-t_0)^2}{2}
+$$
+</p>
+<p style="text-align: center;">
+
+$$
+x = x_1+x_2
+$$
+</p>
+<p style="text-align: center;">
+$$
+x = v_0 t+\frac{a(t-t_0)^2}{2}
+$$
+</p>
+
+ </p>
+
+ <h4>Answer</h4>
+ <p>
+ $$L = v_{0}t + \frac{v_{0} (t − t_{0})^{2}}{2t_{0}}$$
+ </p>
+
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