Which would take more force to stop and 10 seconds 8 kg ball rolling in a straight line at a speed of 0.2 m/s or a 4 kg ball rolling along the same path at a speed of 1 m/s

It takes more force to stop the 4kg ball rolling at 1m/s.

Explanation:

To stop a ball rolling at 0.2 m/s in 10 seconds means the uniform deceleration needs to be (0.2/10) m/s/s = 0.02 m/s^2. To achieve that on a mass of 8kg requires a (force) = (mass) x (acceleration) = (8kg) x (-0.02 m/s^2) = - 0.16 N (negative because it is an opposing force).

To stop a 4kg ball rolling at 1 m/s along the same path as above (implying in 10 seconds of uniform deceleration), will take a deceleration of (1/10 m/s^2) and a (force) = (4kg) x (-0.1 m/s^2) = - 0.4 N.

It takes more force to stop the 4kg ball rolling at 1m/s.

(For your interest: you could decide this question also by calculating which ball has the larger kinetic energy and argue that, consequently, to stop that ball a larger force is needed. Kinetic energy is proportional to the square of force exerted)