The movement of two cars on the highway is given by the equations: x1 = 2t + 6t ^ 2, x2 = 36-4t.

The movement of two cars on the highway is given by the equations: x1 = 2t + 6t ^ 2, x2 = 36-4t. Determine the type of movement of each of the cars. Find the time and place of the meeting.

x1 (t) = 2 * t + 6 * t ^ 2.

x2 (t) = 36 – 4 * t.

tvs -?

hvs -?

With rectilinear uniform motion, the dependence of the coordinate on time x (t) has the form: х (t) = х0 + V * t, where х0 is the initial coordinate, V is the speed of movement.

x2 (t) = 36 – 4 * t – uniform rectilinear movement in the opposite direction of the ox axis with a speed of V = 4 m / s, x20 = 36.

x1 (t) = 2 * t + 6 * t ^ 2 – uniformly accelerated motion at which, x10 = 0 m, V0 = 2 m / s, a = 12 m / s2.

36 – 4 * tvs = 2 * tvs + 6 * tvs ^ 2.

6 * tvs ^ 2 + 6 * tvs – 36 = 0.

tvs ^ 2 + tvs – 6 = 0.

D = 1 – 4 * 1 * (-6) = 25.

tvs = (- 1 + 5) / 2 = 2 s.

xvs = 36 – 4 * 2 = 28 m.

Answer: the bodies will meet after a time tвs = 2 s, at a point with a coordinate xвс = 28 m.