Two freight cars, each with a mass of 3.9 105 kg, collide and stick together. One was initially moving at 3.2 m/s and the other was at rest. What is their final speed in m/s?

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29 To find the final speed of the two freight cars after they collide and stick together, we can use the principle of conservation of momentum.

According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision, provided that no external forces act on the system. Mathematically, this can be represented as:

m1*v1 + m2*v2 = (m1 + m2) * vf

Where:
m1 = mass of the first freight car
v1 = initial velocity of the first freight car
m2 = mass of the second freight car
v2 = initial velocity of the second freight car
vf = final velocity of the combined freight cars

In this case, since one freight car is initially at rest (v2 = 0), the equation becomes:

m1*v1 = (m1 + m2) * vf

Plugging in the given values:

m1 = m2 = 3.9 * 10^5 kg
v1 = 3.2 m/s
v2 = 0 m/s

(3.9 * 10^5 kg) * (3.2 m/s) = (3.9 * 10^5 kg + 3.9 * 10^5 kg) * vf

Solving for vf:

(3.9 * 10^5 kg * 3.2 m/s) / (2 * 3.9 * 10^5 kg) = vf

Simplifying:

(3.9 * 3.2 m/s) / 2 = vf

Final velocity, vf = 6.24 m/s

Therefore, the final speed of the two freight cars after they collide and stick together is 6.24 m/s.