Suppose time t1 and t2 is taken by train in two parts of journey and their distances are S1 and S2 respectively. According to question
S1 + S2 = 4 km ..........(1)
t1 + t2 = 4 min ...........(2)
For part AC, distance
S1 = average velocity x time
From equation (1),
For part AC, from formula v = u + at
v = 0 + a1t1 ⇒ t1 = \(\frac{v}{a_1} = \frac{2}{a_1}\) .............(5)
Similarly for part CB,
0 = v - a2t2 ⇒ t2 = \(\frac{v}{a_2} = \frac{2}{a_2}\) ............(6)
∴ From equation (2),
\(\frac{2}{a_1} + \frac{2}{a_2} = 4\)