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A car stops for a red ligth. The light turns green and the car moves for 3 seconds at a steadily increasing speed. During this time, it travels 20 meters. The car then travels at a constant speed for another 3 seconds for a distance of 30 meters. Finally, when approaching another red light, the car steadily slows to a stop during the next 3 seconds in 15 meters. Create equations with respect to time for the position and velocity of the car at each segment.

  • physics -

    d1 = 0.5a*t^2 = 20 m.
    0.5a*3^2 = 20,
    4.5a = 20,
    a = 4.44 m/s^2.
    V = at = 4.44 m/s^2 * 3 s=13.32 m/s.

    V = d2/t = 30/3 = 10 m/s.
    a = (Vf-Vo)/t = (0-10) / 3=-3.33 m/s^2

    d3 = Vo*t + 0.5a*t^2 = 15 m.
    10*3 + 0.5a*3^2 = 15,
    30 + 4.5a = 15
    4.5a = 15-30 = -15,
    a = --3.33 m/s^2.

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