From points located at a distance of 100 m from each other, two bodies began to simultaneously

From points located at a distance of 100 m from each other, two bodies began to simultaneously move towards each other – the first at a speed of 5 m / s, and the second at a speed of 15 m / s. a) Write the formulas expressing in SI units the dependence of the coordinate on time for each body. b) How long will it take for the bodies to meet? c) What is the modulus of movement of each body before the meeting?

S = 100 m.

V1 = 5 m / s.

V2 = 15 m / s.

x1 (t) -?

x2 (t) -?

hvs -?

S1 -?

S2 -?

Let us take the first body as the reference body, direct the OX coordinate axis in the direction of its movement, to the right.

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

x1 (t) = x01 + V1 * t.

x1 (t) = 5 * t.

x2 (t) = x02 + V2 * t.

x2 (t) = 100 – 15 * t.

When they meet, their coordinates will be the same: x1 (tvs) = x2 (tvs).

5 * tvs = 100 – 15 * tvs.

tvs = 100/20 = 5 s.

hvs = 5 * 5 = 25 m.

S1 = хвс – х01 = 25 m – 0 m = 25 m.

S2 = х02 – хвс = 100 m – 25 m = 75 m.

Answer: х1 (t) = 5 * t, х2 (t) = 100 – 15 * t, tвс = 5 s, хвс = 25 m, S1 = 25 m, S2 = 75 m.