The correct option is A S1+S2
Given, u=0, and let the constant acceleration be a
From 2nd equation of motion we have
S=ut+12at2
So, for first (p−1) sec the displacement of the body is given as
S1=12a(p−1)2
or, S1=a2(p−1)2.......(i)
and, for first (p) sec the displacement of the body is given as
S2=12ap2
or, S2=a2p2........(ii)
Also, we know that the displacement travelled in nth second is given by
Sn=u+a2(2n−1)
⇒ S(p2−p+1)th=a2[2(p2−p+1)−1]
⇒ S(p2−p+1)th=a2[2p2−2p+1]
⇒ S(p2−p+1)th=a2(p−1)2+a2p2
or, from eq (i) & (ii) we get
S(p2−p+1)th=S1+S2