train car a is at rest when it is hit by train car b. the two cars, which have the same mass, are stuck…

train car a is at rest when it is hit by train car b. the two cars, which have the same mass, are stuck together and move off after the collision. how does the final velocity of train cars a and b after the collision compare to the initial velocity of train car b before the collision?\no the final velocity is double train car bs initial velocity.\no the final velocity is the same as train car bs initial velocity.\no the final velocity is half of train car bs initial velocity.\no the final velocity is zero since train car b will stop.

train car a is at rest when it is hit by train car b. the two cars, which have the same mass, are stuck together and move off after the collision. how does the final velocity of train cars a and b after the collision compare to the initial velocity of train car b before the collision?\no the final velocity is double train car bs initial velocity.\no the final velocity is the same as train car bs initial velocity.\no the final velocity is half of train car bs initial velocity.\no the final velocity is zero since train car b will stop.

Answer

Explanation:

Step1: Apply conservation of momentum

Let the mass of each car be $m$, the initial velocity of car A be $v_{A,i}=0$, and the initial velocity of car B be $v_{B,i}$. The final velocity of the combined cars (mass $m + m=2m$) is $v_f$. According to the law of conservation of momentum $m_1v_{1,i}+m_2v_{2,i}=(m_1 + m_2)v_f$. Substituting the values, we get $m\times0+m\times v_{B,i}=(m + m)v_f$.

Step2: Solve for final velocity

The left - hand side of the equation is $mv_{B,i}$, and the right - hand side is $2mv_f$. So, $mv_{B,i}=2mv_f$. Dividing both sides by $2m$, we get $v_f=\frac{v_{B,i}}{2}$.

Answer:

The final velocity is half of train car B’s initial velocity.