Physics

4.18 - Reaction Times

4 min

note 1 of 4

Reaction time and the factors that affect it

Reaction time is how long a person takes to respond to an event - for example, seeing a hazard and braking.
A typical human reaction time is between 0.2 s and 0.9 s.

A person standing calmly beside a sitting lion on the left, then the same person running away in fright on the right, with a stopwatch above an arrow labelled reaction time between them. — The reaction time is the delay between spotting the lion and starting to run.

Factors that increase reaction time

Tiredness
Drugs
Alcohol
Distractions (such as using a mobile phone or talking to passengers)

Reaction time and driving

An alert driver's reaction time in a real driving situation is around 1 s.
The longer the reaction time, the further the vehicle travels before the driver reacts, which increases the thinking distance.

note 2 of 4

Measuring reaction times with the ruler drop test

Reaction times are so short that a stopwatch can't measure them accurately.
Two common methods:
1. A computer-based test (e.g. clicking a mouse when a screen changes colour).
2. The ruler drop test.

Method - Ruler drop test

Sit with your forearm resting on the edge of a table. Another person holds a ruler vertically between your thumb and forefinger, lined up with the zero mark.
Without warning, the person drops the ruler. You catch it between your thumb and finger as quickly as possible.
Read the distance on the ruler at the top of the thumb. The greater this catch distance, the longer the reaction time.

Improving the quality of the results

Repeat the test multiple times, discard anomalies, and calculate a mean catch distance.
Keep control variables the same each time (same ruler, same drop height, same person dropping it).

A hand with thumb and forefinger open at the zero mark of a vertical ruler numbered 0, 1, 2 and 3, labelled ruler and hand.

note 3 of 4

Calculating reaction time from the catch distance

The ruler accelerates under gravity at a constant rate, $g$ .
The catch distance is converted into a reaction time in two steps.

Step 1 - Find the ruler's speed when caught

$v^{2} - u^{2} = 2 a s$

Where:

$v$ = Final speed of the ruler, in metres per second (m/s)
$u$ = Initial speed, which is 0 m/s
$a$ = Acceleration due to gravity, $g$ , in metres per second squared (m/s²)
$s$ = Catch distance, in metres (m)

Step 2 - Find the reaction time

Because the ruler starts from rest, its final speed equals its change in speed ( $Δ v$ ):

$t = \frac{Δ v}{a}$

Where:

$t$ = Reaction time, in seconds (s)
$Δ v$ = Change in speed, in metres per second (m/s)
$a$ = Acceleration due to gravity, $g$ , in metres per second squared (m/s²)

Near the Earth's surface, $g$ ≈ 9.8 m/s² (or 10 m/s²).

note 4 of 4

Worked example - Reaction time from a 30 cm catch

A student does the ruler drop test and catches the ruler at a distance of 30 cm. Calculate the student's reaction time. Take $g$ = 9.8 m/s².

Step 1 - Convert the catch distance to metres

$s = 30 cm = 0.3 m$

Step 2 - Find the speed of the ruler when it is caught

Use $v^{2} - u^{2} = 2 a s$ with $u = 0$ , so $v = \sqrt{2 a s}$ :

$\begin{matrix} v & = \sqrt{2 \times 9.8 \times 0.3} \\ = \sqrt{5.88} \\ = 2.42 m/s \end{matrix}$

Step 3 - Find the reaction time

The ruler started from rest, so the change in speed is $Δ v$ = 2.42 m/s. Rearrange $a = \frac{Δ v}{t}$ to give $t = \frac{Δ v}{a}$ :

$\begin{matrix} t & = \frac{2.42}{9.8} \\ = 0.247 \\ = 0.25 s (to 2 significant figures) \end{matrix}$

key terms

TermDefinition

Reaction timeHow long a person takes to respond to an event.

end of notes

Key points to remember

Measuring reaction times with the ruler drop test

Reaction times are so short that a stopwatch can't measure them accurately.

Two common methods:

A computer-based test (e.g. clicking a mouse when a screen changes colour).
The ruler drop test.

Method - Ruler drop test

Sit with your forearm resting on the edge of a table. Another person holds a ruler vertically between your thumb and forefinger, lined up with the zero mark.

Without warning, the person drops the ruler. You catch it between your thumb and finger as quickly as possible.

Read the distance on the ruler at the top of the thumb. The greater this catch distance, the longer the reaction time.

Improving the quality of the results

Repeat the test multiple times, discard anomalies, and calculate a mean catch distance.

Keep control variables the same each time (same ruler, same drop height, same person dropping it).

Calculating reaction time from the catch distance

The ruler accelerates under gravity at a constant rate,

g

The catch distance is converted into a reaction time in two steps.

Step 1 - Find the ruler's speed when caught

$v^{2} - u^{2} = 2 a s$

Where:

$v$ = Final speed of the ruler, in metres per second (m/s)
$u$ = Initial speed, which is 0 m/s
$a$ = Acceleration due to gravity, $g$ , in metres per second squared (m/s²)
$s$ = Catch distance, in metres (m)

Step 2 - Find the reaction time

Because the ruler starts from rest, its final speed equals its change in speed ( $Δ v$ ):

$t = \frac{Δ v}{a}$

Where:

$t$ = Reaction time, in seconds (s)
$Δ v$ = Change in speed, in metres per second (m/s)
$a$ = Acceleration due to gravity, $g$ , in metres per second squared (m/s²)

Near the Earth's surface, $g$ ≈ 9.8 m/s² (or 10 m/s²).

Worked example - Reaction time from a 30 cm catch

A student does the ruler drop test and catches the ruler at a distance of 30 cm. Calculate the student's reaction time. Take

g

= 9.8 m/s².

Step 1 - Convert the catch distance to metres

$s = 30 cm = 0.3 m$

Step 2 - Find the speed of the ruler when it is caught

Use $v^{2} - u^{2} = 2 a s$ with $u = 0$ , so $v = \sqrt{2 a s}$ :

$\begin{matrix} v & = \sqrt{2 \times 9.8 \times 0.3} \\ = \sqrt{5.88} \\ = 2.42 m/s \end{matrix}$

Step 3 - Find the reaction time

The ruler started from rest, so the change in speed is $Δ v$ = 2.42 m/s. Rearrange $a = \frac{Δ v}{t}$ to give $t = \frac{Δ v}{a}$ :

$\begin{matrix} t & = \frac{2.42}{9.8} \\ = 0.247 \\ = 0.25 s (to 2 significant figures) \end{matrix}$