# The equations of motion of two bodies are x1 = 10t + 0.4, x2 = -6t + 2. find the place

The equations of motion of two bodies are x1 = 10t + 0.4, x2 = -6t + 2. find the place and time of the meeting. what will be their distance in 5s

x1 = 10 * t + 0.4.

x2 = – 6 * t + 2.

t = 5 s.

hvst -?

tvst -?

S -?

S = x1 (t) – x2 (t).

x2 (t) = – 6 * 5 s + 2 = – 28 m.

x1 (t) = 10 * 5 s + 0.4 = 50.4 m.

S = 50.4 m – (- 28 m) = 78.4 m.

The bodies will meet when they have the same coordinates: x1 (t) = x2 (t).

10 * tvst + 0.4 = – 6 * tvst + 2.

16 * twst = 1.6.

tvst = 0.1 s.

We find the coordinate of the meeting хвст by substituting the meeting time tвст into any equation of motion.

hvst = 10 * 0.1 s + 0.4 = 1.4 m.

hvst = – 6 * 0.1 s + 2 = 1.4 m.

Answer: S = 78.4 m, twst = 0.1 s, hvst = 1.4 m.

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