$1.2.4.$ 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.
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.
Any graph with a coordinate change of $20$ m in the specified time and with the greatest “slope” of the tangent $15$ m/s