Question

a bus starts moving from rest with acceleration 1m/s
no useless answer
otherwise;

Answer 1

hello friend!

velocity of man = 10 m/s
s = 42 m
Acceleration of boy = 0 m/s
Acceleration of bus = 1m/s² 

Acceleration of man with respect to bus =
= Acc. of boy - Acc. of bus
= 0 - (1)
= -1 m/s²

using the second law of motion,
s = ut + 1/2 at²
42= 10t - 1/2*t²
20t = 84 + t²
t²-20t + 84 = 0  ( here forming the quadratic equation)
t²-14t - 6t + 84 = 0 (spilliting the middle term)

t = 6sec and t = 14 sec 

by solving we get that :
boy will catch cross the bus after 6 sec 
bus will cross the boy after 14 sec 

hope it helps!

Answer 2

bus will cross the boy after 14 sec
boy will cross the bus after 6 sec

hope this attachment helps you