91Ó°ÊÓ

The center of mass of a system is a point where you can assume all the masses of the system to be situated.

To find the center of mass, you have to consider the two people at the front as one particle and the three people in the back seat as another particle.

The mass of the car is \({m_1} = 1250\;{\rm{kg}}\).

The mass of the people is \(m = 65.0\;{\rm{kg}}\).

The distance of the CM of the empty car is \({x_1} = 2.40\;{\rm{m}}\) behind the front of the car.

The distance of the CM of the people sitting in the front seat is \({x_2} = 2.80\;{\rm{m}}\) behind the car's front.

The distance of the CM of the people sitting in the back seat is \({x_3} = 3.90\;{\rm{m}}\) behind the car's front.

Now, the center of mass of the mass system is:

\(\begin{array}{c}{x_{{\rm{CM}}}} = \frac{{\left( {{m_1} \times {x_1}} \right) + \left( {2m \times {x_2}} \right) + \left( {3m \times {x_3}} \right)}}{{{m_1} + 2m + 3m}}\\ = \frac{{\left( {1250\;{\rm{kg}} \times 2.40\;{\rm{m}}} \right) + \left( {2 \times 65.0\;{\rm{kg}} \times 2.80\;{\rm{m}}} \right) + \left( {3 \times 65.0\;{\rm{kg}} \times 3.90\;{\rm{m}}} \right)}}{{1250\;{\rm{kg}} + \left( {2 \times 65.0\;{\rm{kg}}} \right) + \left( {3 \times 65.0\;{\rm{kg}}} \right)}}\\ = 2.62\;{\rm{m}}\end{array}\)

Hence, the center of mass of the car is \(2.62\;{\rm{m}}\) behind the front of the car.