Final answer:
The final velocity of the other train car, which is moving in the opposite direction, is 1.5 m/sec to the left.
Step-by-step explanation:
When two train cars collide and move off in opposite directions, their total momentum before the collision is equal to their total momentum after the collision. In this case, the first car was initially traveling at a velocity of 2.0 m/sec and the second car was initially traveling at a velocity of 3.0 m/sec to the left. After the collision, the first car is moving at a velocity of 2.5 m/sec to the left. We can use the conservation of momentum to find the final velocity of the second car.
Let's define the right direction as positive and the left direction as negative. The initial momentum of the first car is given by:
M₁,i = m₁ * v₁,i = 10 kg * 2.0 m/sec = 20 kg·m/sec
The initial momentum of the second car is given by:
M₂,i = m₂ * v₂,i = 10 kg * (-3.0 m/sec) = -30 kg·m/sec
The total initial momentum is given by:
M_total,i = M₁,i + M₂,i = 20 kg·m/sec + (-30 kg·m/sec) = -10 kg·m/sec
The final momentum of the first car is given by:
M₁,f = m₁ * v₁,f = 10 kg * (-2.5 m/sec) = -25 kg·m/sec
Using the conservation of momentum, we can find the final momentum of the second car:
M_total,f = M₁,f + M₂,f = -25 kg·m/sec + M₂,f = -10 kg·m/sec
Simplifying the equation, we get:
M₂,f = M_total,f - M₁,f = -10 kg·m/sec - (-25 kg·m/sec) = 15 kg·m/sec
Therefore, the final velocity of the second car is 1.5 m/sec to the left.