Question 107135
Let t=reaction time, x=distance between pin prick and brain, then
{{{T=Ax+B}}}
A and B are constants determined by experimentation.
{{{T=Ax+B}}}
1.{{{15.2=A(100)+B}}} Finger data
2.{{{22.9=A(170)+B}}} Toe data
Use equation 2 to solve for B and substitute into 1.
2.{{{22.9=A(170)+B}}}
{{{B=22.9-A(170)}}}
Now substitute,
1.{{{15.2=A(100)+B}}}
{{{15.2=A(100)+(22.9-A(170))}}}
{{{-7.7=-70A}}}
{{{A=0.11}}}
Now that you know A, find B. 
{{{B=22.9-A(170)}}}
{{{B=22.9-(0.11)(170)}}}
{{{B=4.2}}}
Therefore your equation is
a.){{{T=0.11x+4.2}}}
where x is measured in cm, and T is measured in milliseconds. 
b.) When x=10 cm, then
{{{T=0.11x+4.2}}}
{{{T=0.11(10)+4.2}}}
{{{T=5.3}}}
T=5.3 milliseconds
c.)The time equation is broken up into two sections:length dependent part {{{0.11x}}} and the length independent part {{{4.2}}}. 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.
{{{v=1cm/0.11ms}}}x{{{1000m/s}}}= {{{9090}}} cm/sec
e.)

{{{drawing( 300, 300, -10, 190, -10, 30,grid( 10),green(line( 0,4.2, 200, 26.2)),circle(100,15.2,3),circle(170,22.9,3))}}}