A particle starting from rest accelerates uniformly along a straight horizontal line. The ratio of the distance travelled by the particle in the n^ th second to that in the (n+1)^ th second is 5:7 . What is the value of n ?

Step-by-step solution

For a particle starting from rest ( u = 0 ) and moving with uniform acceleration a , the distance travelled in the n^ th second is given by: S_n = u + a 2 (2n - 1) = a 2 (2n - 1) Similarly, the distance travelled in the (n+1)^ th second is: S_ n+1 = a 2 [2(n+1) - 1] = a 2 (2n + 1) According to the given condition, the ratio of these distances is 5:7 : S_n S_ n+1 = 2n - 1 2n + 1 = 5 7 Cross-multiplying to solve for n : 7(2n - 1) = 5(2n + 1) 14n - 7 = 10n + 5 4n = 12 n = 3 Thus, the value of n is 3 . Answer: 3