A length S is divided into n equal parts, at the end of which, the acceleration of a moving point - Physics - Motion In A Plane

Question

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

Jyoti Pant · Accepted Answer

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

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