Two trains B and C, each 200 m in length, are traveling in the same direction on two parallel straight railway lines. At a certain instant B has a speed of 90 km/h and a deceleration of 0,1 m/s2 and C has a speed of 20 kim/h and an acceleration of 0,2 m/s and the front end of B is in line with the rear end of c. (a) How long will it take before B will just have passed C? (10) (by What is the velocity of B at that instant?​

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