Question

A body is moving from rest under constant acceleration. Let s1 be the displacement in the first (p-1) sec and s2 be the displacement in the first p sec. The displacement in (p^2-p+1)th sec is what ?​

Answer 1

Displacement in first (p−1) sec,

S1=12a(p−1)2−−−(I)

Displacement in p sec,

S2=12ap2−−−−−(ii)

(Using, s=ut+12at2 and putting initial velocity, u=0)

Adding (i) and (ii)

S1+S2=12a(p−1)2+12ap2

=12a[2p2−2p+1]−−−−−−(a)

Displacement in (p2−p+1) th second is given by

S=12a[2(p2−p+1)−1]

=12a[2p2−2p+1]−−−−−

−(b)

From (a) and (b)

S=S1+S2