In the figure here, a red car and a green car move toward each other in adjacent

Question

In the figure here, a red car and a green car move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 217 m. If the red car has a constant velocity of 22.0 km/h, the cars pass each other at x = 43.2 m. On the other hand, if the red car has a constant velocity of 44.0 km/h, they pass each other at x = 76.3 m. What are (a) the initial velocity (in km/h) and (b) the (constant) acceleration (in m/s2) of the green car? Include the signs.

Explanation / Answer

Vr = 22km/h * 1m/s / 3.6km/h = 6.11 m/s: Sr =43.2 m = 6.11m/s * t ? this tells us t = 7.07s Sg = 43.2 m = 217m + Vg * t + ½at² Plug in for t: 43.2= 217+ 6.11Vg + 18.66a -6.11Vg = 173.8 + 18.66a Vg = -28.45 - 3.05a ? for later Vr = 44km/h * 1m/s / 3.6km/h = 12.22m/s: Sr = 76.3m = 12.22m/s * t ? t = 6.24s Sg = 76.3m = 217m + Vg * t + ½at² Sub for t and Vg: 76.3 = 217 + (-28.45 - 3.05a)(6.24) + ½a(6.24)² 76.3 = 217 -177.53 - 19.03a + 19.47a 36.83 = -0.44 a a = -83.7 m/s² ? acceleration Vg = -28.45- 3.05(-83.7) = -226.84m/s

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