First slide

Instantaneous acceleration

Question

A small block slides without friction down an inclined plane starting from rest. Let S_n be the distance travelled from time t = n -1 to t = n. Then [S_n/(S_n+1)] is

Easy

A

$\frac{(2 n - 1)}{2 n}$
B

$\frac{(2 n + 1)}{(2 n - 1)}$
C

$\frac{(2 n - 1)}{(2 n + 1)}$
D

$\frac{2 n}{(2 n + 1)}$

Solution

The displacement from t = n - 1 tot = n is given by
$∴ {(S_{n})}_{th} = (\frac{a}{2}) (2 n - 1)$
The body starts from rest, i.e., u = 0
$∴ {(S_{n})}_{th} = (\frac{a}{2}) (2 n - 1)$
Then $\frac{S_{n}}{S_{n + 1}} = \frac{(\frac{a}{2}) (2 n - 1)}{(\frac{a}{2}) [2 (n + 1) - 1]} = \frac{(2 n - 1)}{(2 n + 1)}$

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