Draw a graph of coordinate versus time for a rectilinear motion that satisfies two conditions simultaneously: a. the average speed in the time interval from 2 to 6 s is 5 m/s; b. the maximum speed in the same interval is 15 m/s.

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    <h3> Statement </h3>
    <p>
        $1.2.4.$ Draw a graph of coordinate versus time for a rectilinear motion that satisfies two conditions simultaneously: 

a. the average speed in the time interval from $2$ to $6$ s is $5$ m/s;

b. the maximum speed in the same interval is $15$ m/s.

    <h3>Solution</h3>
    <p>
            It is necessary to choose such a dependence so that the derivative of the coordinate in time, aka velocity, obeys the conditions of the problem.

An example of such a function is shown at the bottom:

The derivative of $x(t) = 2.5t^2-15t$ is equal to

$v(t) = 5t-15$

What satisfies the conditions of the problem.

    <h4>Answer</h4>
    <p>
        Any graph with a coordinate change of $20$ m in the specified time and with the greatest “slope” of the tangent $15$ m/s
    </p>


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