A particle moves with uniform acceleration along a straight line from rest. The percentage increase in displacement during sixth second compared to that in fifth second is about

The displacement of a particle moving with uniform acceleration from rest (u=0) during the nth second is given by the formula S_n = u + a/2(2n - 1). For a particle starting from rest, this simplifies to S_n = a/2(2n - 1). Calculating the displacement for the fifth second (n=5), we get S_5 = a/2(2*5 - 1) = 9a/2. For the sixth second (n=6), the displacement is S_6 = a/2(2*6 - 1) = 11a/2. The increase in displacement from the fifth to the sixth second is S_6 - S_5 = (11a/2) - (9a/2) = 2a/2 = a. To find the percentage increase compared to the fifth second, we use the formula: ((S_6 - S_5) / S_5) * 100. This results in (a / (9a/2)) * 100 = (2/9) * 100, which is approximately 22.22%. Thus, the percentage increase is about 22%.