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A 1100 kg automobile is at rest at a traffic signal. At the instant the light turns green, the automobile starts to move with a constant acceleration of 3.0 m/s2. At the same instant a 2800 kg truck, traveling at a constant speed of 8.0 m/s, overtakes and passes the automobile. (a) How far is the center of mass of the automobile–truck system from the traffic light at t= 3.0s? (b) What is the speed of the center of mass of the automobile-truck system then?

  • physics help -

    First write the location of the auto and of the truck as a function of time after the light turns green (t). Call these locations X1 and X2.

    X1 = 1.5 t^2 (the auto)
    X2 = 8.0 t (the truck)

    The center of mass location is
    X3 = (1100 X1 + 2800 X2)/3900.

    The speed of the CM is dX3/dt
    V3 = [1100*3t + 2800*8]/3900

    Finish the calculation

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