The left ventricle of the heart accelerates blood from rest to a velocity of +21.4 cm.
A. If the displacement of the blood during the acceleration is +1.55 cm, determine its acceleration (in cm/s2).
B. how much time does the blood take to reach its final velocity?
To determine the acceleration of the blood in the left ventricle, you need to use the equation of motion. The equation that relates velocity (v), initial velocity (u), acceleration (a), and displacement (s) is as follows:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
A. To find the acceleration, we need to rearrange the equation and solve for a:
a = (v^2 - u^2) / (2s)
Given:
v = +21.4 cm (final velocity)
u = 0 cm (initial velocity because the blood starts from rest)
s = +1.55 cm (displacement)
Substituting the values into the equation, we have:
a = (21.4^2 - 0^2) / (2 * 1.55)
a = (456.96) / (3.1)
a ≈ 147.742 cm/s^2
Therefore, the acceleration of the blood in the left ventricle is approximately 147.742 cm/s^2.
B. To find the time taken for the blood to reach its final velocity, we can use the equation of motion:
v = u + at
Rearranging the equation to solve for time (t):
t = (v - u) / a
Using the given values:
v = +21.4 cm
u = 0 cm
a = 147.742 cm/s^2
Substituting the values into the equation, we have:
t = (21.4 - 0) / 147.742
t ≈ 0.145s
Therefore, it takes the blood approximately 0.145 seconds to reach its final velocity.