The problem states that a particle is moving with uniform acceleration along a straight line, starting from rest. We are asked to find the percentage increase in displacement during the sixth second compared to that in the fifth second.

When a particle moves with uniform acceleration, its displacement is given by the formula:

S = ut + (1/2)at^2, where S is the displacement, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time.

To compare the displacements in the fifth and sixth seconds, we need to find the displacement at the end of each second. Let`s represent the displacement at the end of the fifth second as S5 and the displacement at the end of the sixth second as S6.

Using the formula, we have:

S5 = (1/2)a(5)^2 = 12.5a

S6 = (1/2)a(6)^2 = 18a

To find the percentage increase in displacement, we need to calculate the difference between S6 and S5 as a percentage of S5:

Percentage increase = [(S6 - S5)/S5] * 100

= [(18a - 12.5a)/(12