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Motion in a Straight Line — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsMotion in a Straight Line1 Mark
Question
Reaction time : When a situation demands our immediate action, it takes some time before we really respond. Reaction time is the time a person takes to observe, think and act. For example, if a person is driving and suddenly a boy appears on the road, then the time elapsed before he slams the brakes of the car is the reaction time. Reaction time depends on complexity of the situation and on an individual.
You can measure your reaction time by a simple experiment. Take a ruler and ask your friend to drop it vertically through the gap between your thumb and forefinger (Fig. 2.8). After you catch it, find the distance $d$ travelled by the ruler. In a particular case, $d$ was found to be $21.0 cm$. Estimate reaction time.
✓

Answer

The ruler drops under free fall. Therefore, $v_o=0$, and $a=-g=-9.8 m s ^{-2}$. The distance travelled $d$ and the reaction time $t_r$ are related by
$
\begin{array}{l}
d=-\frac{1}{2} g t_r^2 \\
t_r=\sqrt{\frac{2 d}{g}} s
\end{array}
$
Given $d=21.0 cm$ and $g=9.8 m s ^{-2}$ the reaction time is
$
t_r=\sqrt{\frac{2 \times 0.21}{9.8}} s \equiv 0.2 s .
$

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