IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

# Reaction Time

## Introduction

The distance travelled by a freely falling object can be used as a sensitive measure of short time intervals. This demo is based on kinematic equation $$s=ut+\frac{1}{2}at^2$$, where $$s$$ is the distance travelled, $$u$$ is the initial speed, $$a$$ is the acceleration, and $$t$$ is the time.

meter scale

## Procedure

The demonstration consists of holding a meter scale vertically from the top while a volunteer stands ready to catch it between the thumb and forefinger. If the fingers are opposite the 50 cm mark, for example, when the meter scale is dropped, the position of the fingers when the meter scale is caught gives a measure of the distance the meter scale fell before the volunteer could react. The time is then calculated from $$t=\sqrt{2s/g}$$, where $$g=9.8\,\mathrm{m/s^2}$$ and $$s$$ is the distance dropped (in meters). If $$s=20\,\mathrm{cm}$$ then we get $$t=0.2\, \mathrm{s}=200\,\mathrm{ms}$$.

## Discussion

We observed that students generally makes two mistakes (i) incorrect measurement of distance travelled (ii) forget to convert distance from centimetre to metre before use in the formula.