Three points are located at the vertices of an equilateral triangle whose side equals $a$. They all start moving simultaneously with velocity $v$ constant in modulus, with the first point heading continually for the second, the second for the third, and the third for the first. How soon will the points converge?

An elevator car whose floor to ceiling distance is equal to $2.7 \mathrm{m}$, starts ascending with constant acceleration $1.2 \mathrm{m} {\mathrm{s}}^{-2}, 2.0 \mathrm{s}$, after the start a bolt begins falling from the ceiling of the car. Find, 
$\left(a\right)$ the bolt's free-fall time,
$\left(b\right)$ the displacement and the distance covered by the bolt during the free-fall in the reference frame fixed to the elevator shaft.

(Take $g=9.8{\mathrm{ms}}^{-2}$)

From point $A$ located on a highway (as shown) one has to get by car as soon as possible to point $B$ located in the field at a distance from the highway. It is known that the car moves in the field $\eta$ times slower than on the highway. At what distance from point $D$ one must turn off the highway?

A point travels along the $x$-axis with a velocity whose projection $v_{\mathrm{x}}$ is presented as a function of time by the plot.

Assuming the coordinate of the point $x=0$ at the moment $t=0$, draw the approximate time dependence plots for the acceleration $w_{\mathrm{x}}$, the $x$ coordinate and the distance covered $s$.