The distance S travelled by a particle is calculated using the formula $S = u t - \frac{1}{2} a t^{2}$ If there is 1% error in t, then approximate percentage error in S is

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$\frac{1}{2} (\frac{u - a t}{2 u - a t})$

$2 (\frac{u - a t}{2 u - a t})$

$(\frac{u - a t}{2 u - a t})$

$(\frac{u - a t}{3 u - a t})$

answer is B.

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Detailed Solution

$S = u t - \frac{1}{2} a t^{2} \Rightarrow \log S = \log [u t - \frac{1}{2} a t^{2}]$

$\Rightarrow \frac{1}{s} δ S = \frac{1}{u t - \frac{1}{2} a t^{2}} [u δ t - \frac{1}{2} a (2 t) δ t]$

$= \frac{2}{t (2 u - a t)} [u . δ t - \frac{1}{2} a (2 t) δ t]$

$\Rightarrow \frac{2}{(2 u - a t)} [u \cdot \frac{δ t}{t} - a t \cdot \frac{δ t}{t}]$

$\Rightarrow \frac{δ S}{S} \times 100 = \frac{2}{2 u - a t} [u - a t] \frac{δ t}{t} \times 100 = \frac{2 (u - a t)}{2 u - a t}$

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