Question

an empty 2,500 kg train car is headed northbound at a velocity of 5 m/s. ahead of the first car, an empty 1,500 kg car is headed northbound on the same track at 1 m/s. the faster train bumps into the slower one, and they combine into one train. what is the velocity of the two - car train? 1 m/s 3 m/s 3.5 m/s 5 m/s

Explanation:

Step1: Apply conservation of momentum

$m_1v_1 + m_2v_2=(m_1 + m_2)v$
$m_1 = 2500$ kg, $v_1 = 5$ m/s, $m_2 = 1500$ kg, $v_2 = 1$ m/s
$(2500\times5+1500\times1)=(2500 + 1500)v$

Step2: Solve for $v$

$v=\frac{2500\times5+1500\times1}{2500 + 1500}=\frac{12500+1500}{4000}=\frac{14000}{4000}=3.5$ m/s

Answer:

C. 3.5 m/s