The center of mass of the car with all people seated will be 3.20 m far from the front of the car.
Taking the front of the car as reference:
m₁x₁ + m₂x₂ + m₃x₃ = mx
where,
m₁ = mass of empty car = 1300 kg
x₁ = distance of center of mass of empty car from front = 2.45 m
m₂ = mass of 2 people sitting in front = 2 x 60 kg = 120 kg
x₂ = distance of center of mass of 2 people sitting in front from the front = 2.7 m
m₃ = mass of 3 people sitting in back seat = 3 x 60 kg = 180 kg
x₃ = distance of center of mass of 3 people sitting in the back seat from the front = 3.65 m
m = total mass of car with all people = 1300 kg + 120 kg + 180 kg = 1600kg
x = distance of center of mass of the car from the front when all are seated
Therefore,
(1300 kg)(2.45 m) + (120 kg)(2.7 m) + (180kg)(3.65 m) = (1300 kg)x
x = 4166 kg.m/1300 kg
x = 3.20 m
Therefore, the center of mass of the car with all people seated will be 3.20 m far from the front of the car.
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