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.

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <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 $t > t_0$.

    <h3>Solution</h3>
    <p>
        

At time $t_0$, the coordinate was $x_1=v_0t_0$.

On the interval from $t_0$ to $2t_0$, the acceleration is constant and equal to $a=\frac{v_0}{t_0}$.

In the case of equiaxcelerated motion with initial velocity $v_0$ from time $t_0$, the path is found as

$$x_2 = v_0 (t-t_0)+\frac{a(t-t_0)^2}{2}$$

$$x = x_1+x_2$$

$$x = v_0 t+\frac{a(t-t_0)^2}{2}$$

    </p>

    <h4>Answer</h4>
    <p>
        $$L = v_{0}t + \frac{v_{0} (t − t_{0})^{2}}{2t_{0}}$$
    </p>


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