Brain teaser 4
A particle starts its motion from rest and moves with uniform acceleration. If it travels a distance 'S' in first 1 second of its motion, then the distance traveled in the 2nd second of its motion is 'nS'. What is n?
NOTE: 2nd second means the distance traveled in first 2 second minus Distance traveled in first 1 second
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1 solution
let s(n) be the distance travelled in the nth second. s(n)=u+[(2n-1)a/2] where "u" is the initial velocity and "a" is the acceleration. since the particle starts from rest,u=0. for first 1second, S=a/2, For 2nd second, nS=3a/2, by solving we get n=3.