Hello!

As I understand, the rocket backpack provides a constant force of `100 N.` During its work it throws away some mass, therefore the mass of the astronaut with his equipment changes. We don't know how it changes, but I suppose that this change is small (negligible).

The mass `m` of an astronaut with his space suit is his weight on Earth divided by Earth's gravitational acceleration `g=9.8 m/s^2.` His mass is `200 kg.` The mass remains the same in space, while weight may change even on Earth (during a free fall, for example).

By Newton's second law, the astronaut gets a constant acceleration of `a=F/m=100/200=0.5(m/s^2),` where `F` is a force. Therefore his velocity is `V(t)=at` and his displacement is `d(t)=(a t^2)/2` (because the initial speed is zero).

Thus, after `3` seconds the velocity will be `0.5*3=1.5 (m/s)` and the distance will be `(0.5*9)/2=2.25 (m).`