Question

1. A body is moving from rest under constant acceleration and let \( S_{1} \) be the displacement in the first \( (p-1) \sec \) and \( S_{2} \) be the displacement in the first \( P \sec \). The displacement in \( \left(p^{2}-p+1\right)_{t h} \) sec. will be (1) \( S_{1}+S_{2} \) (2) \( S _{1} S _{2} \) (3) \( S_{1}-S_{2} \) (4) \( S _{1} / S _{2} \)

Answer 1

HELLO,

Let the constant acceleratin be \(a\)

According to the question we have:

\(S_1=\frac{1}{2}a(p-1)^2\)    --------- (1)

\(S_2=\frac{1}{2}a(p)^2\)          ---------- (2)

Displacement in \((p^2-p+1)_{th} \) sec (\(S_0\))  = Dislacement in first \((p^2-p+1)\) sec - Displacement in first \((p^2-p) \) sec

\(S_0=\frac{1}{2}a(p^2-p+1)^2-\frac{1}{2}a(p^2-p)^2\)

\(S_0=\frac{1}{2}a[(p^4+p^2+1-2p^3+2p^2-2p)-(p^4+p^2-2p^3)]\)

\(S_0=\frac{1}{2}a[1+2p^2-2p]\)

\(S_0=\frac{1}{2}a[1+p^2+p^2-2p]\)

\(S_0=\frac{1}{2}a[(p^2+1-2p)+(p^2)]\)

\(S_0=\frac{1}{2}a(p-1)^2+\frac{1}{2}a(p)^2\)

from equation (1) and (2) we get;

\(S_0=S_1+S_2\)

Hence, the correct option is (1)

I HOPE YOU WILL UNDERSTAND.