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Q.
A body covers $12\,m$ in $3rd$ second of its linear uniformly accelerated motion. It covers $20\,m$ in the $5th$ second. Velocity of the body after $10\,s$ is
Motion in a Straight Line
Solution:
Using, $S_n = u+\frac{1}{2}a(2n-1),$
we get $12=u+\frac{a}{2}(2\times3-1)$
$=u+2.5\,a \quad...(i)$
Also, $20=u+\frac{a}{2}(2\times5-1)$
$=u+4.5\,a \quad ...(ii)$
Solving (i) and (ii) $a \,= 4ms^{-2}$
Using (i), we get $12 = u + \frac{4}{5}\times5$
$i.e\,\,u=2ms^{-1}$
From the relation $\upsilon = u + at,$
we get, $\upsilon = 2 + 4 \times 10 = 42 ms^{-1}$