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28 March, 07:06

Two cars drive on a straight highway. At time t=0, car 1 passes mile marker 0 traveling due east with a speed of 20.0 m/s. At the same time, car 2 is 0.80 km east of mile marker 0 traveling at 26.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 0.40 m/s^2, and car 2 is slowing down with an acceleration of magnitude 0.80 m/s^2. a.) Write x-versus-t equations of motion for both cars, taking east as the positive direction.

b.) At what time do the cars pass next to one another?

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  1. 28 March, 07:53
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    a) Equation for car 1

    X = 20 t + 1/2 x 0.40 t² (initial velocity is 20 and acceleration is 0.4)

    Equation for car 2

    X = 800 - (26 t - 1/2 x0.80 t²) [ when t = 0, X = 800 m and with time t, X decreases ]

    b) Let after time t they meet, then X will be equal for both of them at t.

    20 t + 1/2 x 0.40 t² = 800 - (26 t - 1/2 x0.80 t²)

    0.20 t² - 46 t + 800 = 0

    t = 19 s and 211 s.
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