Question

. Two trains each of length 100m, moving in opposite directions along parallel lines meet, their speeds 60 km/h and 30 km/h. If their accelerations are 30 cm/s2 and 20 cm/s2 respectively. The time they take to pass each
other is
1) 50 s
2) 57.44 s
3) 435
4) 7.44s
​

Answer 1

answer : option (4) 7.44 sec

explanation : let trains cross each other after time t,

so, distance travelled by first train, $S_1=u_1t+\frac{1}{2}a_1t^2$

here, $u_1$ = 60km/h = 60 × 5/18 = 50/3 m/s

$a_1$ = 30cm/s² = 30 × 10^-2 m/s² = 0.3 m/s²

so, $s_1$ = (50/3)t + 1/2 × (0.3)t² ....(1)

similarly, distance travelled by 2nd train, $S_2=u_2t+\frac{1}{2}a_2t^2$

here, $u_2$ = 30km/h = 30 × 5/18 = 25/3 m/s

$a_2$ = 20cm/s² = 20 × 10^-2 m/s² = 0.2m/s²

so, $s_2$ = (25/3)t + 1/2(0.2)t².....(2)

trains will cross each other after time t only when,

$s_1+s_2=100+100$

or, (50/3)t + 1/2(0.3)t² + (25/3)t + 1/2(0.2)t² = 200

or, 25t + 1/2(0.5)t² = 200

or, 100t + t² = 800

or, t² + 100t - 800 = 0

or, t = {-100 ± √{100² + 4 × 800}}/2

≈ 7.44sec

hence, option (4) is correct choice.