A neuron in your brain sends a charge down an 80 cm long axon (a long skinny thing) toward your hand at a speed of 10 m per second. At the time when the charge reaches your elbow, the voltage in the axon is -70 mV except on the 6 cm long piece between 47 and 53 cm from your brain. On this piece, the voltage is
v(x) = -70.0 + 10.0[9.0 - (x - 50.0)2]
where v(x) is the voltage at a distance of x centimeters from the brain.
a. How long will it take the information to get to your hand? How long did it take to reach your elbow?
b. Sketch a graph of the voltage along the whole axon.
c. Find the average voltage of the 6 cm piece.
d. Find the average voltage of the whole axon.