Two people of equal mass attempt a tug-of-war with a 10 m long rope while standing on ice. On pulling the rope, they both slide towards
each other. What will be the acceleration for each person?

When they pull on the rope, they each slide toward each other. How do their accelerations compare and how far does each person slide before they meet? The force on each will be the same so they will always have the same acceleration -- and, because of that, the same velocity and they will move the same distance.

Explanation:

As the poster has noted above in comment, the acceleration for each person will be the same. This is because when they tugon the rope, there will be tension force on the rope pulling the two persons towards each other. The tension force will be the same for them. As they also have equal mass, by Newton's Second Law of Motion, Force = mass * acceleration, their acceleration will be the same.

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