The two cars were moving towards each other at speeds of 60 km / h and 40 km / h
The two cars were moving towards each other at speeds of 60 km / h and 40 km / h, being initially at a distance of 150 km. Determine the coordinate and time of the meeting, if they started at the same time.
v1 = 60 km / h – speed of the first car;
v2 = 40 km / h – speed of the second car;
L = 150 kilometers – distance between cars.
It is required to determine the X coordinate and the meeting time t of cars.
Let the first car start moving from the coordinate X = 0. Then its equation of motion will be:
x1 (t) = v1 * t.
The second car starts moving from the X = L coordinate and moves towards the first car, then its equation of motion will be:
x2 (t) = L – v2 * t.
To find the meeting time, let us equate both equations of motion, since at the meeting point their coordinates will be equal:
x1 (t) = x2 (t);
v1 * t = L – v2 * t;
L = v1 * t + v2 * t;
L = t * (v1 + v2);
t = L / (v1 + v2) = 150 / (60 + 40) = 150/100 = 1.5 hours.
To find the coordinate of the meeting, we substitute the value of t into any equation of motion:
x = v1 * t = 60 * 1.5 = 90 kilometers.
Answer: cars will meet at point X = 90 kilometers in 1.5 hours after the start of movement.