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25 February, 21:36

Two cars pass each other traveling at the same speed. one car has a constant velocity of 15.0 m/s, east. the other car has a constant acceleration of 1.00 m/s, west. how much time will have elapsed until the cars are 164 m apart?

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  1. 26 February, 00:53
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    The formula for calculating the distance at constant velocity is:

    d = v * t

    d = 15 t

    The formula for distance at constant acceleration is:

    d = v0 t + 0.5 a t^2

    d = 15 t + 0.5 t^2

    So after a sum distance of 164 m:

    15 t + (15 t + 0.5 t^2) = 164

    30 t + 0.5 t^2 = 164

    t^2 + 60 t = 328

    (t + 30) ^2 = 328 + 30^2

    t + 30 = ± 35.04

    t = - 65.04, 5.04

    Since time cannot be negative, so the two cars are 164 m apart after about 5 seconds
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