physics

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A train is moving parallel and adjacent to a
highway with a constant speed of 22 m/s. Initially a car is 69 m behind the train, traveling
in the same direction as the train at 35 m/s
and accelerating at 3 m/s
2
.
What is the speed of the car just as it passes
the train

  • physics -

    D1 = D2 - 69.
    V*t = Vo + 0.5at^2 -69,
    22t = 35t + 0.5 * 3t^2 - 69,
    22t = 35t + 1.5t^2 - 69,
    22t - 1.5t^2 - 35t = -69,
    -1.5t^2 -13t + 69 = 0,
    Multiply both sides by -1:
    1.5t^2 + 13t - 69 = 0.
    Using Quadratic Formula,

    t = (-13 +- sqrt(169 + 414)) / 3,
    t = (-13 +- 24.1) / 3,
    t = 3.72, and -12.37.
    Use the positive value of t:
    t = 3.72s.

    V = Vo + at = 35 + 3 * 3.72 = 46.12m/s.

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