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15 May, 22:20

At the instant a traffic light turns green, a car starts from rest with a given constant acceleration of 0.5 m/s squared. Just as the light turns green, a bus, traveling with a given constant speed 16.0 m/s, passes the car. The car speeds up and passes the bus sometime later. How far down the road has the car traveled when the car passes the bus?

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  1. 16 May, 01:08
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    d = 1024 m

    Explanation:

    Kinematics of the car

    The car moves with uniformly accelerated movement we apply the following formula:

    d = v₀t + (1/2) * a*t² Formula (1)

    Where:

    d:displacement in meters (m)

    t : time in seconds (s)

    v₀: initial speed in m/s

    a: acceleration in m/s²

    Data

    v₀₁ = 0 : initial speed of the car

    a₁ = 0.5 m/s² : acceleration of the car

    Kinematics equation of the car

    We replace data in the formula (1):

    d = 0 + (1/2) * 0.5*t²

    d = (0.25) * t² Equation (1)

    Kinematics of the bus

    The car moves with uniformly movement (constant speed) we apply the following formulas:

    d = v*t Formula (2)

    Where:

    d:displacement in meters (m)

    t : time in seconds (s)

    Data

    v = 16 m/s

    Kinematics equation of the bus

    We replace data in the formula (2):

    d = 16*t Equation (2)

    Problem development

    when the car passes the bus the elapsed time (t) and the distance (d) is equal for both.

    Equation (1) = Equation (2) = d

    (0.25) * t² = 16*t We divide both sides of the equation by t

    (0.25) * t = 16

    t = 16 / (0.25)

    t = 64 s

    We replace t in the equation (2)

    d = 16*t

    d = 16 * (64)

    d = 1024 m
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