Question

hey

see the attachment given

Answer 1

Assuming the man is moving with constant speed :
Final Constant speed : 6m/s

Question will be much easier if we go for Relative motion.

u (rel) = 0
a(rel) = 3m/s^2
S(rel) = 6m

Now, using
Newtons law of Equation,

${v(rel)}^{2} = \: {u(rel)}^{2} + 2as \\ v(rel) = \sqrt{ {0}^{2} + 2 \times 3 \times 6 } \\ = > v(rel) = 6 \frac{m}{s} \\ therefore \: man \: shoud \: run \: with \\ \: speed \: \: at \: least \: 6metre \: per \: seond \\ to \: catch \: the \: bus$



hope, you understand my answer.
Have A wonderful day.