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?

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>
        $1.2.8^*.$ 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:

$$v_0 = \frac{L}{t}$$

During the deceleration interval the velocity changes as

$v(t) = v_0-at \Rightarrow v_0=at$

Equating the equations, we obtain

$L=at^2$

From where

$v_0 = \sqrt{La}$

    <h4>Answer</h4>
    <p>
        $$v = \sqrt{La}$$
    </p>


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