The graph in which the block will travel with the greatest speed is the graph with the greatest displacement at given equal forces.
Work energy theorem
Based on the principle of work energy theorem, the work done in moving the block against the frictionless floor is equal to the kinetic energy.
K.E = ¹/₂kx²
K.E = ¹/₂Fd
¹/₂mv² = ¹/₂Fd
mv² = Fd
v² = Fd/m
v = √ (Fd/m)
Thus, the graph in which the block will travel with the greatest speed is the graph with the greatest displacement at given equal forces.
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