A length S is divided into n equal parts, at the end of which, the acceleration of a moving point is increased by f/n. Find the velocity of the poin after describing the distance s given that the particle started from rest with acceleratin f. EXPLAIN

Suppose v1,v2....vn are the velocities at the end of the first, second,...nth interval respectively.Since the acceleration during these intervals are,f,(f+fn),(f+2fn).....,(f+n-1nf)and the length of each interval is sn, we havev12=02+2f.sn  (using equation of motion)v22=02+2(f+fn).snv32=02+2(f+2fn).sn.....................................................................vn2=vn-12+2(f+n-1nf).snAdding vertically,vn2=2f.sn[1+(1+1n)+(1+2n)+.....+(1+n-1n)]=2f.sn[n+1+2+3+......+(n-1)n]=2f.sn[n+(n-1)n2n]=2f.sn(3n-12)vn=fs(3n-1)n

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