5 cars moving at a speed of 2.4 m / s collide and couple with three stationary cars.

5 cars moving at a speed of 2.4 m / s collide and couple with three stationary cars. At what speed will the cars move after coupling if the mass of all cars is the same?

Given:

v = 2.4 meters per second – the speed of the cars;

n1 = 5 is the number of moving cars;

n2 = 3 – the number of stationary cars.

It is required to determine v1 (meter per second) – the speed of the cars after coupling.

According to the problem statement, the mass of all cars is the same. Then, according to the law of conservation of momentum (momentum), we find:

n1 * m * v = (n1 + n2) * m * v1, where m is the mass of the cars.

n1 * v = (n1 + n2) * v1

v1 = n1 * v / (n1 + n2) = 5 * 2.4 / (5 + 3) = 12 / (5 + 3) = 12/8 = 1.5 meters per second.

Answer: the speed of the cars after coupling will be equal to 1.5 meters per second.