Two points move along the X axis, the coordinates of which change

Two points move along the X axis, the coordinates of which change according to the laws x = 10 + 2t and x = 4-5t. The points will meet at the moment of time …

x1 (t) = 10 + 2 * t.

x2 (t) = 4 – 5 * t.

tvs -?

hvs -?

1 way.

With uniform rectilinear motion, the coordinate of the body changes according to the law x (t) = x0 + V * t, where x0 is the initial coordinate of the body, V is the speed of uniform motion.

For the dependence x1 (t) = 10 + 2 * t, the initial coordinate is x10 = 10, the speed of movement is V1 = 2. The speed with the “+” sign means that the first body moves to the right side, along the ОХ axis.

For the dependence x2 (t) = 4 – 5 * t, the initial coordinate is x20 = 4, the speed of movement is V2 = -5.

The “-” sign means that the body moves in the opposite direction to the direction of the OX axis.

The second body has an initial coordinate x20 = 4, which is located to the left of the initial coordinate of the first body, x10 = 10, and moves to the left. The bodies will not meet.

Method 2.

The points will meet at that moment in time when their coordinates are equal: x1 (tvs) = x2 (tvs).

10 + 2 * tvs = 4 – 5 * tvs.

7 * tvs = – 6.

tvs = – 6/7 s.

We see that the time of movement cannot be negative. From the moment the observation begins, the bodies will not meet.

Answer: bodies will not meet.