Reaction Time
Roy Coleman Morgan Park High School
Retired
Objective:
Each student will be able to obtain his/her reaction time by making simple
measurements. Each student will also be able to find the constituent parts of
their overall reaction time.
Materials needed:
Each group of two will need one 30 cm (12 inch) ruler to find their reaction
time. For the more advanced activities, each group will need a meter stick, a
stopwatch and two funnels connected together by more than two meters of rubber
tubing.
Suggested Strategy:
The time that it takes you to react to a particular situation is called your
reaction time. Your reaction time depends on many factors including the
stimulus and the particular part of the body that is to react, i.e., it takes
longer to move your foot from the gas to the brake pedal than it does for your
fingers to grab something simply because your leg is heavier and it has to move
farther.
Today we will be finding the time required for you to grab a dropped object,
namely a 12 inch ruler. Brace your hand on the edge of a desk so that the
fingers are over the edge ready to grab the ruler as it is dropped. Have your
partner hold the ruler such that its zero centimeter mark is even with the
center of your fingers and, at some random time, drop it. Record the distance
that the ruler fell (where you caught it), during the time that your body was
reacting. Do this at least 10 times. It is important that the ruler is held
even with your fingers (not above or below them) and that it is dropped (not
thrown down). ALL readings MUST be recorded but any readings that are way out
of line can be crossed out and ignored. (In general, your measurements should
be between 10cm and 30cm.) Average your readings and then determine your
reaction time.
The reaction time can be determined in several ways. You can use the standard
equation for freely falling bodies Sf=1/2at2+vot+So. Where Sf is the average
distance that the ruler fell, a is the acceleration of gravity (980 cm/sec2),
t is the time that it takes the ruler to fall (the reaction time), vo is the
initial velocity (zero) and So is the initial distance (zero). Substituting in
zero for vo and So simplifies this to Sf=1/2at2. Solving this equation for t
yields
dt=sqrt(2Sf/a)
An alternate method would be to use the following chart to look up the time
corresponding to the average distance that the ruler fell.
DISTANCE TIME DISTANCE TIME DISTANCE TIME DISTANCE TIME
(cm) (sec) (cm) (sec) (cm) (sec) (cm) (sec)
0.012 -- 0.005 8.281 -- 0.130 31.862 -- 0.255 70.756 -- 0.380
0.049 -- 0.010 8.930 -- 0.135 33.124 -- 0.260 72.630 -- 0.385
0.110 -- 0.015 9.604 -- 0.140 34.410 -- 0.265 74.529 -- 0.390
0.196 -- 0.020 10.302 -- 0.145 35.721 -- 0.270 76.452 -- 0.395
0.306 -- 0.025 11.025 -- 0.150 37.056 -- 0.275 78.400 -- 0.400
0.441 -- 0.030 11.772 -- 0.155 38.416 -- 0.280 80.372 -- 0.405
0.600 -- 0.035 12.544 -- 0.160 39.800 -- 0.285 82.369 -- 0.410
0.784 -- 0.040 13.340 -- 0.165 41.209 -- 0.290 84.390 -- 0.415
0.992 -- 0.045 14.161 -- 0.170 42.642 -- 0.295 86.436 -- 0.420
1.225 -- 0.050 15.006 -- 0.175 44.100 -- 0.300 88.506 -- 0.425
1.482 -- 0.055 15.876 -- 0.180 45.582 -- 0.305 90.601 -- 0.430
1.764 -- 0.060 16.770 -- 0.185 47.089 -- 0.310 92.720 -- 0.435
2.070 -- 0.065 17.689 -- 0.190 48.620 -- 0.315 94.864 -- 0.440
2.401 -- 0.070 18.632 -- 0.195 50.176 -- 0.320 97.032 -- 0.445
2.756 -- 0.075 19.600 -- 0.200 51.756 -- 0.325 99.225 -- 0.450
3.136 -- 0.080 20.592 -- 0.205 53.361 -- 0.330 101.442 -- 0.455
3.540 -- 0.085 21.609 -- 0.210 54.990 -- 0.335 103.684 -- 0.460
3.969 -- 0.090 22.650 -- 0.215 56.644 -- 0.340 105.950 -- 0.465
4.422 -- 0.095 23.716 -- 0.220 58.322 -- 0.345 108.241 -- 0.470
4.900 -- 0.100 24.806 -- 0.225 60.025 -- 0.350 110.556 -- 0.475
5.402 -- 0.105 25.921 -- 0.230 61.752 -- 0.355 112.896 -- 0.480
5.929 -- 0.110 27.060 -- 0.235 63.504 -- 0.360 115.260 -- 0.485
6.480 -- 0.115 28.224 -- 0.240 65.280 -- 0.365 117.649 -- 0.490
7.056 -- 0.120 29.412 -- 0.245 67.081 -- 0.370 120.062 -- 0.495
7.656 -- 0.125 30.625 -- 0.250 68.906 -- 0.375 122.500 -- 0.500
Another alternative would be to draw a graph from the above chart and have the
students read the time from the graph.
The experiment could be stopped at this point but there are several more things
that can be calculated. The time obtained in the first part (call it reaction
time-tr) is really the sum of three other times: 1) the time that it takes for
your brain to realize that the object has been dropped (call it processing time-
tp); 2) the time for the nerve signal to travel from your brain to your fingers
(call it nerve time-tn); and 3) the time that it takes for your fingers to close
(call this dynamic time-td). (i.e., tr=tp+tn+td)
The easiest of the three to calculate is the nerve time (tn). Since nerve
signals travel at an approximate speed of 30,000 cm/sec, we can measure the
distance from your brain to your fingers and use the equation time=distance/rate
to find the nerve time.
The next easiest is dynamic time (td). Dynamic time can be found by using a
timer with a second hand or stopwatch to time 25 complete pinches (open and
close) and then dividing that time by 50 (since each open and close is two
actions).
Processing time (tp) can be found two ways. One method is to work backwards
from the reaction time. Given tr, tn and td, you can subtract the sum of tn and
td from tr to get the processing time. An alternate way that should produce a
result that is within the same order of magnitude is to take the tubing with a
funnel in each end. Mark the center of the tubing. Have a student sit with one
funnel over each ear and the tubing spread behind them. Have the partner tap the
tubing at various places and ask the listener to indicate which ear/side the tap
was on. There will be a dead spot near the middle where the listener cannot tell
which side the tap was on. Mark the approximate locations (left side and right
side) of the limits of the dead spot. The length of the dead spot can be used to
find the processing time. Knowing the speed of sound is about 34,000cm/sec,
time=distance/speed can be used to determine th brain's processing time. In
addition, some anatomy can be determined because, for most people, the dead spot
will not be centered but slightly off to one side. That is due to the fact that
the brain's auditory processing area is located on one side and it takes a tiny
bit longer for the signals to travel from the ear furthest from the autitory
center.
Performance Assessment:
Several large sheets of paper should be hung on the wall of the classroom about
knee level. Each sheet should have the outline of a gas pedal and brake pedal
drawn on the sheet. Each group of students should be able to determine their
reaction time and dynamic time for moving their foot off of the gas to the
brake. First hint: Hold the meterstick even with the top of the brake pedal and drop
it. Students can then move their foot to 'catch' the meterstick with their foot
similar to dropping the ruler between the fingers. Second hint: make sure the
classroom wall is sturdy enough to take some kicking.
Multicultural Note:
All of the equations and symbols used in this lesson are the same, regardless of
the language of instruction. Ukranian, German, Italian and Japanese physics
books all have their physics equations in 'English'.
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