The graph with the largest displacement at given equal forces is the one in which the block travels with the fastest speed.
According to the work-energy theorem, the net work done by forces on an item equals the change in its kinetic energy.
The work done in pushing the block against the frictionless floor is equal to the kinetic energy, according to the work-energy theorem. Therefore,
K.E = ¹/₂kx²
K.E = ¹/₂Fd
¹/₂mv² = ¹/₂Fd
mv² = Fd
v² = Fd/m
v = √(Fd/m)
Thus, the graph with the largest displacement at equal forces is the one in which the block travels the fastest.
Learn more about the Work-energy Theorem:
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