I dont need the work shown I just need the answers in the

A 1500 kg automobile is at rest at a traffic signal. At theinstant the light turns green, the automobile starts to move with a constant acceleration of 3.0 m/s2. At the same instant a 2700 kg truck, traveling at a constant speed of 9.0 m/s, overtakes and passes the automobile. (a) How far is the com of the automobile-truck system from the traffic light at t = 3.0 s? 25 (b) What is the speed of the center of mass of the com then? m/s

Solution

At t = 3.0 s, position of the automobile is x₁ = ½ at² = 13.5 m

v₁ = a t = 9 m/s

The truck moves at constant velocity v₂. At t = 3.0 s is position is x₂ = v₂ t = 27 m

speed is 9.0 m/s

a) The position of the center of mass is

x = (m₁x₁ + m₂x₂)/(m₁ + m₂)

= (1500*13.5 + 2700*27)/(1500 + 2700)

= 22.18 m

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b) The velocity of the center of mass is

v = (m₁v₁ + m₂v₂)/(m₁ + m₂)

= (1500*9 + 2700*9)/(1500 + 2700)

= 9 m/s