Solve analytically and then check graphically.
Velocity of Blood Because of friction from the walls of an artery, the velocity of a blood corpuscle in an artery is greatest at the center of the artery and decreases as the distance r from the center increases. The velocity of the blood in the artery can be modeled by the function
v = k(R2 − r2)
where R is the radius of the artery and k is a constant that is determined by the pressure, viscosity of the blood, and the length of the artery. In the case where k = 2 and R = 0.1 centimeter, the velocity is v = 2(0.01 − r2) centimeters per second (cm/sec).
a. What distance r would give a velocity of 0.02 cm/ sec?
b. What distance r would give a velocity of 0.015 cm/sec?
c. What distance r would give a velocity of 0 cm/sec? Where is the blood corpuscle?
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