a vehicle that weighs 4000N on the surface of the earth is travelling in outer space at a speed of 200m/s.?

The smallest constant force that must be applied to stop it in 20 seconds is?

force × time = (change in momentum)

change in momentum = mass × (final speed − initial speed).

They give you the "time", the "initial speed" and the "final speed"; and the "mass" is just (weight / g). Solve for "force".

You need to figure the impulse to stop the vehicle.

Impulse = change in momentum
Force x time, applied = mass x change in velocity

1. You need to find the mass of the vehicle. You're given the weight of the vehicle 4000 N, but you know that the acceleration of gravity at sea level is about 9.81 m/s^2

Use Force = ma and solve for m.

2. Now that you know m, you can solve for Force since you know time,applied, initial velocity and final velocity.

Force x time, applied = mass x change in velocity
F x 20 = m (v,final - v, initial)

You finish the rest of the work.

The mass of the vehicle = 4000/9.8 =408.16 kg.
Acceleration = [v-u] / t = [0 - 200] /20 = - 10m/s^2.
Force = mass x acceleration = 408.16* [- 10] = - 4081.6 N.
Negative sign shows that the force is opposite to the velocity.