Question

Two cars each with mass $M$ are heading towards each other, one with velocity $v_1=-2m/s$ and the other with $v_2=3m/s$.
What is the speed of the center of mass of the two-car system?

• A. $\frac{1}{2}m/s$
• B. $1m/s$
• C. $\frac{3}{2}m/s$
• D. $\frac{5}{2}m/s$
• E. $5m/s$

Answer 1

The correct option is A $\frac{1}{2}m/s$

Given : $m_1=m_2=M$ $v_1=-2$ m/s $v_2=3$ m/s

Speed of centre of mass $V_{CM}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}$

$\therefore$ $V_{CM}=\frac{M(-2)+M\left(3\right)}{M+M}=\frac{1}{2}$ m/s