The left ventricle of the heart accelerates blood from rest to a velocity of +23 cm/s.
(a) If the displacement of the blood during the acceleration is +2.1 cm, determine its acceleration (in cm/s2).
(b) How much time does blood take to reach its final velocity? in seconds
To find the acceleration of the blood, we can use the equation:
v^2 = u^2 + 2as
where:
v = final velocity = +23 cm/s
u = initial velocity = 0 cm/s (since the blood starts from rest)
s = displacement = +2.1 cm
(a) Rearranging the equation, we get:
a = (v^2 - u^2) / 2s
Substituting the given values:
a = (23^2 - 0^2) / (2 * 2.1) = 529 / 4.2 ≈ 126.19 cm/s^2
Therefore, the acceleration of the blood is approximately 126.19 cm/s^2.
Now, to find the time it takes for the blood to reach its final velocity, we can use the equation:
v = u + at
where:
v = final velocity = +23 cm/s
u = initial velocity = 0 cm/s
a = acceleration = 126.19 cm/s^2 (as calculated above)
t = time
(b) Rearranging the equation, we get:
t = (v - u) / a
Substituting the given values:
t = (23 - 0) / 126.19 ≈ 0.1825 seconds
Therefore, it takes approximately 0.1825 seconds for the blood to reach its final velocity.