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?

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    <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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