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Question

A body is moving from rest under constant acceleration and let S1 be the displacement in the first (p1) sec and S2 be the displacement in the first p sec. The displacement in (p2p+1)th sec will be


Correct Answer
A
S1+S2
Your Answer
B
S1S2
Your Answer
C
S1S2
Your Answer
D
S1S2

Solution

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 (p1) sec the displacement of the body is given as
S1=12a(p1)2
or, S1=a2(p1)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(2n1)
 S(p2p+1)th=a2[2(p2p+1)1]
 S(p2p+1)th=a2[2p22p+1]
 S(p2p+1)th=a2(p1)2+a2p2
or, from eq (i) & (ii) we get
S(p2p+1)th=S1+S2
 

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