Question 107135: Reaction time problem: When you are pricked with a pin, there is a short time delay before you say "ouch!" This reaction time varies linearly with the distance between your brain and the place you are pricked. Dr. Hollers pricks Leslie Morley's finger and toe, and measures reaction times of 15.2 and 22.9 milliseconds, respectively. (A millisecond is 1/1000 of a second.) Leslie's finger is 100 cm from the brain, and her toe is 170 cm from the brain.
a) Write the particular equation expressing time delay in terms of distance.
b) How long would it take Leslie to say "ouch" if pricked in the neck, 10 cm from the brain?
c) What does the time-intercept equal, and what does it represent in the real world?
d) Since the slope is in millisecons per centimeter, its reiprocal is the speed whick nerve impulses travel in centimetes per millisecond. How fast do the impulses travel in cm/sec?
e) Sketch and label the gragh.
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Let t=reaction time, x=distance between pin prick and brain, then
A and B are constants determined by experimentation.
1. Finger data
2. Toe data
Use equation 2 to solve for B and substitute into 1.
2.
Now substitute,
1.
Now that you know A, find B.
Therefore your equation is
a.)
where x is measured in cm, and T is measured in milliseconds.
b.) When x=10 cm, then
T=5.3 milliseconds
c.)The time equation is broken up into two sections:length dependent part  and the length independent part  . The length dependent part is the time it takes the signal to travel from the injury to the brain. The length independent part is the time required for the brain to recognize there is an injury and to send a signal to your speech center and then make the sound, "Ouch".
d.) Slope = 0.11 ms/cm, velocity,v, is 1/Slope.
 x =  cm/sec
e.)
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