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Q.
A particle starting with certain initial velocity and uniform acceleration covers a distance of $12\,m$ in first $3$ seconds and a distance of $30\, m$ in next $3$ seconds. The initial velocity of the particle is
Given,
$s_{1}=12\, m , t_{1}=3\, s $
$s_{2}=30+12=42\, m $
$t_{2}=3+3=6 \,s$
$\therefore s=u t+\frac{1}{2} \,a t^{2}$
$\therefore s_{1} =u t_{1}+\frac{1}{2}\, a t_{1}^{2} $
$ 12=3 \times u+\frac{1}{2} a \times 3^{2} $
$ 12=3 u+\frac{9}{2} a \,\,\,...(i)$
Similarly, $ u^{2}=6 u+\frac{1}{2} a\, 36\,\,\,...(ii)$
Solving the Eqs. (i) and (ii), we get
$a=2\, m / s ^{2}, $
$u=1 \,m / s$
$u$ is initial velocity.