Two blocks a and b ($m_a> m_b$) are pushed for a certain distance along a frictionless surface. how does the magnitude of the work that a does on b compare to the magnitude of the work that b does on a?

the magnitude of the work done by the two blocks is the same.

Explanation:

The work done by block a on block b is given by:

where Fa is the force exerted by block a on block b, and d is the distance they cover.

The work done by block b on block a is given by:

where Fb is the force exerted by block b on block a, and d is still the distance they cover.

For Newton's third law, the force exerted by block a on block b is equal to the force exerted by block b on block a, therefore

and so

the independent variable, or the one that is intentionally manipulated is the speed.

a. are