Explanation:
A Given,
\(\mathrm{s}_{1}=200 \mathrm{~cm}, \quad \mathrm{~s}_{2}=220 \mathrm{~cm}\)
\(\mathrm{t}_{1}=2 \mathrm{sec}, \quad \mathrm{t}_{2}=4 \mathrm{sec}\)
\(\mathrm{t}=7 \mathrm{sec}\)
\(\mathrm{I}^{\text {st }}\) condition,
\(s=u t+\frac{1}{2} a t^{2}\)
\(200=u \times 2+\frac{1}{2} a(2)^{2}\)
\(200=2 \mathrm{u}+2 \mathrm{a}\)
\(100=\mathrm{u}+\mathrm{a} \ldots\)
II \(^{\text {nd }}\) condition,
\(\mathrm{s}_{3}=\mathrm{ut}_{3}+\frac{1}{2} \mathrm{at}_{3}^{2}\)
\(420=\mathrm{u} \times 6+\frac{1}{2} \times \mathrm{a}(6)^{2}\)
\(420=6(\mathrm{u}+3 \mathrm{a})\)
\(70=\mathrm{u}+3 \mathrm{a} \ldots \ldots . . \text { (ii) }\)
\(\mathrm{s}_{3}=\mathrm{s}_{1}+\mathrm{s}_{2}=420 \mathrm{~m}, \mathrm{t}_{3}=\mathrm{t}_{1}+\mathrm{t}_{2}=2+4=6 \mathrm{sec}\)
From equation (i) and (ii), we get
\(100-70=4+a-4-3 a\)
\(30=-2 a\)
\(a=-15 \mathrm{~m} / \mathrm{s}^{2}\)
From equation (ii),
\(\mathrm{u}+3(-15)=70\)
\(\mathrm{u}=115 \mathrm{~m} / \mathrm{s}\)
Now,
\(\mathrm{v}=\mathrm{u}+\mathrm{at}\)
\(\mathrm{v}=115+(-15) \times 7\)
\(\mathrm{v}=10 \mathrm{~m} / \mathrm{s}\)