A body starts from rest and moves with a uniform acceleration. The ratio of the distance covered by the body in the n ^ th second of its motion to the total distance travelled in n second is

Step-by-step solution

A body starts from rest with uniform acceleration of magnitude a . The distance covered in the n ^ th second is S_n^ th = u + a 2 (2n - 1) . With initial velocity u = 0 , this becomes S_n^ th = a 2 (2n - 1) . The total distance traveled in n seconds is S_n = 1 2 an^2 . The ratio is then S_n^ th S_n = a 2 (2n - 1) 1 2 an^2 = 2n - 1 n^2 , which simplifies to 2 n - 1 n^2 . The correct option is C.