The graph of the velocity of the body versus time looks like a semicircle. Maximum velocity of the body v_0, time of motion t_0. Determine the distance traveled by the body.

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>
        $1.2.6.$ The graph of the velocity of the body versus time looks like a semicircle. Maximum velocity of the body $v_0$, time of motion $t_0$. Determine the distance traveled by the body.

    <h3>Solution</h3>
    <p>
        The traveled path can be found as the area under the graph $v(t)$. If the area of the semicircle $S=\pi r^2/2$, then the required path:

$$x = \frac{\pi v_0t_0}{4}$$

    <h4>Answer</h4>
    <p>
        $$x = (\pi /4)v_0t_0$$
    </p>


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