Answer:
Explanation:
20 km/hr = 5.56 m/s
90 km/hr = 25 m/s
To have just passed C, B must gain first the length of C, then the length of B for a total 400 m
s = s₀ + v₀t + ½at²
if s₀ = 0 at the head of train C when t = 0
for train C, the position in time is
s = 0 + 5.56t + ½(0.2)t²
s = 5.56t + 0.1t²
for train B which must gain 400 m in the same time
s = -400 + 25t + ½(-0.1)t²
s = -400 + 25t - 0.05t²
As both equations equal s, we can set the other sides equal
5.56t + 0.1t² = -400 + 25t - 0.05t²
0.15t² - 19.44t + 400 = 0
quadratic formula positive answer
t = (19.44 + √(19.44² - 4(0.15)(400))) / (2(0.15))
t = 104 s
v = 25 + 104(-0.1) = 14.6 m/s or 52.6 km/hr
