A body is moving from rest under constant acceleration and let s1
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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
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
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