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  4. A body starts from rest, what is the ratio of the distance travelled by the during the 4 textth and 3 textrd second ?

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Q. A body starts from rest, what is the ratio of the distance travelled by the during the $4^{\text{th}}$ and $3^{\text{rd}}$ second ?

AIPMTAIPMT 1993Motion in a Straight Line

Solution:

Distance covered in $n^{\text{th}}$ second is given by
$ S_n = u + \frac{a}{2} (2n - 1)$
Here, u = 0
$\therefore S_4 = 0 + \frac{a}{2} (2 \times 4 - 1)=\frac{7a}{2}$
$S_3 = 0 + \frac{a}{2} (2 \times 3 - 1)=\frac{5a}{2} $
$\therefore \frac{S_4}{S_3}=\frac{7}{5}$