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13 January, 01:03

At the instant the traffic light turns green, an automobile starts with a constant acceleration a of 2.20 m/s^2. At the same instant a truck, traveling with a constant speed of 8.50 m/s, overtakes and passes the automobile. (a) How far beyond the traffic signal will the automobile overtake the truck? (b) How fast will the automobile be traveling at that instant?

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  1. 13 January, 01:08
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    a) d=65.7 m : The automobile overtake passes the truck at a distance of 65.7 m from the traffic signal

    b) vₐ=16.94m/s : Automobile speed for t = 7.7s

    Explanation:

    When the car catches the truck, the two will have passed the same time (t) and will have traveled the same distance (d):

    Automobile kinematics:

    car moves with uniformly accelerated movement:

    d = v₀*t + (1/2) a*t²

    v₀ = 0 : initial speed

    d = (1/2) * a*t² Equation (1)

    Truck kinematics:

    Truck moves with constant speed:

    d = v*t Equation (2)

    dа ta:

    a=2.20 m/s² : automobile acceleration

    v = 8.50 m/s; truck speed

    Equation (1) = Equation (2)

    (1/2) * a*t² = v*t

    (1/2) * 2.2*t² = 8.5*t We divide both sides of the equation by t:

    1.1*t=8.5

    t=8.5:1.1

    t=7.7 s

    We replace t=7.7 s in the equation (2)

    d=8.5*7.7

    d=65.7 m

    Automobile speed for t = 7.7s

    vₐ=v₀₊a*t

    vₐ=o₊2,2*7.7

    vₐ=16.94m/s
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