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  4. A body moving with uniform acceleration describes 12 m in the third second of its motion and 20 m in the 5th second. Find the velocity after 10 th second.

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Q. A body moving with uniform acceleration describes 12 m in the third second of its motion and 20 m in the 5th second. Find the velocity after 10 th second.

Jharkhand CECEJharkhand CECE 2011

Solution:

$ {{S}_{n}}=u+\frac{a}{2}(2n-1) $
$ 12=u+\frac{a}{2}(2\times 3-1) $ ..(i)
and $ 20=u+\frac{a}{2}(2\times 5-1) $ ..(ii)
Subtract Eq. (i) from Eq. (ii)
$ 8=\frac{a}{2}(9-5)=2a $
$ \Rightarrow $ $ a=4m/{{s}^{2}} $
From Eq. (i) $ 12=u+\frac{4}{2}\times 5 $
$ u=2\,m/s $
Velocity $ v=u+at=2+4\times 10 $
$ =42\,m/s $