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Reaction times and vehicle stopping distances
gcse physics revision notes
What is your reaction time?
Reaction time
is the time it takes for your body to respond to a stimulus.
Your reaction time is a
measure of how quickly a message is sent and processed by the nervous
system - from detection by receptors to response by effectors (e.g.
muscles).
Simple reaction
time experiments
Your reaction time to a situation may be typically 0.2 to
0.8 seconds when fully alert. However your reaction time can be affected by
tiredness, feeling unwell, drugs, alcohol, in other words anything that
affects the speed of your brain function.
You can conduct quite simple experiments to test your
reaction time to a particular situation. However, since the reaction time is
too short.
(i)
Computer screen reaction test - responding as quickly as possible to
something appearing on the screen.
In this situation, the computer
software generates something up on the screen and your click the mouse
or tap the keypad in response to the visual (or sound?) stimulus.
The computer automatically times
your response by monitoring your contact with the keyboard or by
clicking the mouse - its more accurate, especially as it can measure
reaction times in milliseconds.
Computer generated stimuli give more
accurate response reaction times than e.g. the dropped ruler experiment
described in section (b) which potentially involves human error -
computer experiments avoid the possibility of the person anticipating
when the event is to happen e.g. reading the body language of someone
dropping the ruler in experiment (b) described below.
I've quickly written an extremely
simple computer programme to test your response to a X appearing on
the screen.
Response time
test: It probably only works on Microsoft platforms, and
maybe not all of them?
Your anti-virus protection might
query it, because it is a .exe file, but its written with
compiled BBC BASIC and should not pose any threat. Unfortunately I
never learned to write in a multi-platform professional computer
programming language, but I'm not exactly short of website projects!
(ii)
Catching a falling object test
Fraught with human error, but a bit
of classroom fun!
You get someone to hold a ruler vertically, with
thumb and first finger, above someone else's hand, who is ready to catch
it with their thumb and first finger.
First image on the right. The
ruler should be held at the top of the scale and steady hands from
both people.
The catching person should have
the middle of their thumb and finger adjacent to zero on the cm
scale - squat down to make sure you are reading the scale
horizontally.
Then, without warning, the person holding the ruler,
lets go of it. The second person has to react as fast as possible and
catch the dropped ruler between their thumb and first finger.
Second image on the right.
The
longer the distance d, the slower your reaction time!
When caught, you then read how far
the ruler as fallen by taking the reading, to the nearest centimetre,
from where the middle of their thumb and finger are.
You repeat the experiment a number
of times to get an average, but its not a particularly accurate
experiment.
You need to have steady hands and not
let the ruler wobble about or fall at an angle other than vertical.
Controlling variables - fair test
criteria:
You should drop the ruler from
the same height each time the experiment is performed.
You
should also use the same ruler and the same hand to catch the ruler.
Use the same person/people
dropping the ruler and catching it though, obviously, you can compare
one person's results with another.
The slower your response time, the
further the ruler falls before being caught.
You might repeat the
experiment by having e.g.
having some background distractions - a group of people
talking nearby, or somebody trying to engage you in conversation or
music playing,
or taking a caffeinated drink
like coffee or cola to act as a stimulant. - a drug that speeds up
neural activity in the central nervous system.
Extension of experimental
results
You can pool class results and
produce a histogram of number of pupils versus equally spaced
reaction times.
You can do the same thing
with a computer screen test too.
You can investigate the effect of
stimulant like caffeine in coffee.
i.e. do the test 10 times,
have a rest, drink a cup of coffee and later repeat the test.
You should find that you a
bit faster, a smaller response time because caffeine is a
central nervous stimulant. It makes you more alert.
How to calculate the response
time from your results
There is a simple formula you can
use to calculate the actual reaction time (t in s) from the
distance the ruler falls (d in m), under the acceleration due
to gravity (a = 9.81 m/s2).
t = √(2d / a) =
√(2d / 9.81)
e.g. if the ruler falls 10 cm
(0.10 m), reaction time = √(2 x 0.1 / 9.81) = √ =
0.14 s
Where does the reaction time
formula come from?
Don't worry, you don't have to
know this for either your GCSE/IGCSE biology or physics exams!,
but here is the derivation for my own satisfaction and perhaps some
keen students too?
KEY: a = acceleration (= g =
9.8 m/s2), u = initial velocity (m/s), v =
final velocity (m/s), t = time (s), d = distance (m)
If a body is moving with an
initial velocity of u and accelerates in a uniform manner
(constant acceleration a),
the increase in velocity in a
time is given by: t = at.
Therefore the final velocity v
after time t is given by
(equation 1)
v = u + at
Now, if a body is moving with
uniform acceleration its average velocity is equal to half of
the sum of the initial velocity u and final velocity v.
average velocity = (u + v)
/ 2
but from equation (1),
v = u + at, and substituting in the above equation gives
(equation 2) average
velocity = (u + u + at) / 2 =
u + ˝at
Now the distance d, moved
(displacement) = average velocity x time (remember v = ∆d
/ ∆t)
so, d = (u + ˝at) x t
and, multiplying out gives
(3):
d = ut + ˝at2
now in the experiment, u =
0, so the equation simplifies to (4):
d = ˝at2
this can now be rearranged to
give equation (5):
t = √(2d
/ a)
which is the equation you can
use to calculate your actual reaction time from how far the
ruler fell before you stopped it.
