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19 August, 21:26

A 1050 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 3.3 m/s2. At the same instant a 2200 kg truck, traveling at a constant speed of 9.0 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 = 2.5 s? (b) What is the speed of the center of mass of the automobile-truck system then?

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  1. 19 August, 21:55
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    a. 18.56m

    b. 8.76m/s

    Explanation:

    We would be using the equations from Newton's laws to determine the position of the automobile, the automobile speed and the truck's position

    Note that:

    a = Constant acceleration = 3.3m/s²

    t = 2.5s

    Automobile position we would use this equation

    S = ut + 1/2at²

    Where u = 0

    S = 0 + 1/2 * 3.3 * (2.5) ²

    Sa = 10.31m

    Automobile speed

    v = u + at

    Where u = o

    v = 0 + (3.3 * 2.5)

    v = 8.25m/s

    Truck position,

    From the question constant speed of the truck = 9.0m/s

    S = vt

    St = 9.0 * 2.5.

    = 22.5m

    a. How far is the center of mass of the automobile-truck system from the traffic light at t = 2.5 s?

    (MaSa + MtSt) / Mass of the system

    Where Ma = Mass of the automobile = 1050kg

    Mt = Mass of the truck = 2200kg

    Sa = 10.31m

    St = 22.5m

    Mass of the system = Mass of automobile + Mass of truck

    = 1050 + 2200kg

    = 3250kg

    = (1050 * 10.31) + (2200 * 22.5) / 3250

    = 60325.5 : 3250

    = 18.56m

    b. What is the speed of the center of mass of the automobile-truck system then?

    Speed of the center of mass of an automobile-truck system =

    = (MaVa + MtVt) / Mass of the system

    Where Ma = Mass of the automobile = 1050kg

    Mt = Mass of the truck = 2200kg

    Va = Automobile speed = 8.25m/s

    Vt = Constant speed of the truck = 9.0m/s

    Mass of the system = Mass of automobile + Mass of truck

    = 1050 + 2200kg

    = 3250kg

    = (1050 * 8.25) + (2200 * 9.0) / 3250

    = 28462.5 : 3250

    = 8.76m/s
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