The left ventricle of the heart accelerate blood from rest to a velocity of +24.2 cm/s. (a) if the displacement of the blood during the acceleration is +1.73 cm, determine its acceleration (in cm/s2). (b) How much time does blood take to reach its final velocity?
To solve this problem, we can use the following kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity = +24.2 cm/s
u = initial velocity = 0 cm/s (since blood starts from rest)
a = acceleration (to be determined)
s = displacement = +1.73 cm
(a) Rearranging the equation, we get:
a = (v^2 - u^2) / (2s)
a = (24.2^2 - 0^2) / (2 * 1.73)
a = 294.64 cm^2/s^2 / 3.46 cm
a ≈ 85.12 cm/s^2
So, the acceleration of the blood is approximately 85.12 cm/s^2.
(b) We can use the following kinematic equation to find the time:
v = u + at
Where:
v = final velocity = +24.2 cm/s
u = initial velocity = 0 cm/s (since blood starts from rest)
a = acceleration = 85.12 cm/s^2 (from part a)
t = time (to be determined)
Rearranging the equation, we get:
t = (v - u) / a
t = (24.2 - 0) / 85.12
t = 0.2849 seconds
So, the blood takes approximately 0.2849 seconds to reach its final velocity.