On the coordinate line 1 the body is at -30 m and moves at a speed of 5 ms, 2 the body on the coordinate line

On the coordinate line 1 the body is at -30 m and moves at a speed of 5 ms, 2 the body on the coordinate line is at 60 m and moves at a speed of 1 ms, the bodies move towards each other. Find the time of collision and the place.

x10 = – 30 m.

V1 = 5 m / s.

x20 = 60 m.

V2 = 5 m / s.

hvs -?

tvs -?

Since the bodies move uniformly rectilinearly, the equation of rectilinear uniform motion has the form: х (t) = х0 + V * t. Where x0 is the coordinate of the initial position of the body, V is the speed of movement.

x1 (t) = x10 + V1 * t.

x1 (t) = – 30 + 5 * t.

x2 (t) = x20 + V2 * t.

x2 (t) = 60 – 5 * t.

We will assume that the first body moves in the direction of the ОХ axis, the second body moves in the opposite direction.

When they meet, their coordinates will be equal: x1 (t) = x2 (t).

– 30 + 5 * tvs = 60 – 5 * tvs.

10 * tvs = 90.

tvs = 9 s.

hvs = – 30 + 5 * 9 = 15 m.

Answer: the bodies will meet through tвс = 9 s at the point with the coordinate хвс = 15 m.