Human Reaction Times

1. Person A holds a 30 cm or metre ruler vertically so the 0 cm mark is at the bottom.
2. Person B places their open thumb and first finger level with the 0 cm mark, without touching the ruler.
3. Person A releases the ruler without warning, and Person B catches it as quickly as possible.
4. The distance the ruler fell is read from the top of the thumb or finger.

To ensure reliability, the test must be repeated several times to calculate a mean distance and spot anomalies. A larger distance fallen indicates a slower reaction time.

Experimental Variables and Errors

When planning or explaining this investigation in an exam, you must clearly identify the variables.

• Independent variable: The factor you are testing, such as adding a distraction (e.g., listening to music).
• Dependent variable: The distance the ruler falls (which determines the reaction time).
• Control variables: Factors kept constant for a fair test, such as using the same starting height, the same ruler, and the same catching hand.

Two main errors can affect your results. A parallax error occurs if you do not read the ruler scale exactly at eye level. A zero error happens if the 0 cm mark is not perfectly aligned with the catcher's fingers before the drop.

Calculating Reaction Time from Distance

As the ruler falls, it accelerates downwards due to gravity ($g$). Because it starts from rest, the distance fallen ($d$) is directly proportional to the square of the time taken ($t^2$). You can calculate the exact reaction time using the formula derived from the constant acceleration equations:

$$t = \sqrt{\frac{2d}{g}}$$

Where:

• $t$ = reaction time (s)
• $d$ = distance the ruler fell (m)
• $g$ = acceleration due to gravity, usually taken as $10\text{ m/s}^2$ (or $9.8\text{ m/s}^2$ for higher precision)

Worked Example

A student catches a dropped ruler at a mark of 20 cm. Calculate their reaction time. Assume acceleration due to gravity is $10\text{ m/s}^2$.

Step 1: Identify and convert the values into standard units.

• $d = 20\text{ cm} = 0.2\text{ m}$
• $g = 10\text{ m/s}^2$

Step 2: Substitute the values into the equation.

• $t = \sqrt{\frac{2 \times 0.2}{10}}$

Step 3: Calculate the final answer.

• $t = \sqrt{\frac{0.4}{10}} = \sqrt{0.04} = \mathbf{0.2\text{ s}}$

Computer-Based Methods

While the ruler drop test is easy, it is prone to human error. Digital methods use reaction time software and a digital timer to record the exact time between a visual or auditory stimulus (like a screen changing colour or a beep) and a mouse click.

• Digital methods are far more precise, measuring to the nearest millisecond ($0.001\text{ s}$).
• They remove the "human error" of the person dropping the ruler, who might accidentally give a physical cue.
• The software can use randomized delays between stimuli so the subject cannot anticipate the event.

Factors Affecting Reaction Time

Various everyday factors can change a person's reaction time, which directly impacts road safety.

• Slower reactions (increased time): Caused by tiredness, alcohol, depressant drugs, or distractions (like using a mobile phone).
• Faster reactions (decreased time): Caused by stimulants like caffeine.

Your reaction time determines your thinking distance (the distance a vehicle travels while the driver reacts). Because $\text{Thinking Distance} = \text{Speed} \times \text{Reaction Time}$, a slower reaction time increases the thinking distance. This, in turn, increases the total stopping distance of the vehicle.