Figure ( a ) shows a red car and a green car that move toward each other. Figure
ID: 2168384 • Letter: F
Question
Figure (a) shows a red car and a green car that move toward each other. Figure (b) is a graph of their motion, showing the positionsxg0= 270 m andxr0= -35 m at timet= 0. The green car has a constant speed of 20 m/s and the red car begins from rest. What is the acceleration magnitude of the red car?
Explanation / Answer
Vr = 26km/h * 1m/s / 3.6km/h = 7.22 m/s: Sr =44.7 m = 7.22m/s * t ? this tells us t = 44.7/7.22 s = 6.19s Sg = 44.7 m = 210m + Vg * t + ½at² Plug in for t: 44.7 = 210 + 6.19Vg + 19.15a -6.19Vg = 165.3 + 19.15a Vg = -26.7 - 3.09a ? for later Vr = 52km/h * 1m/s / 3.6km/h = 14.44 m/s: Sr = 76.1m = 14.44m/s * t ? t = 5.27 s Sg = 76.1m = 210m + Vg * t + ½at² Sub for t and Vg: 76.1 = 210 + (-26.7 - 3.09a)(5.27) + ½a(5.27)² 76.1 = 210 - 140.7 - 16.3a + 13.9a 6.8 = -2.4 a a = -2.83 m/s² ? acceleration Vg = -26.7 - 3.09(-2.83) = -17.9 m/s ? initial velocity
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