Human Reaction Times

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:

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.