The left ventricle of the heart accelerates blood from rest to a velocity of +26 cm/s.
(a) If the displacement of the blood during the acceleration is +1.9 cm, determine its acceleration (in cm/s2).
(b) How much time does it take for the blood to reach its final velocity?
d = v * t,
1.9cm = 26cm/s * t,
t = 1.9/26 = 0.073 sec.
Acc. = (Vt - Vo) / t = (26cm/s - 0) / 0.073s = 356.2cm/s^2
(a) Vfinal = sqrt(2aX)
a = Vfinal^2/(2X) = 178 cm^2/s
(b) T = Vfinal/a = 0.15 s
To solve this problem, we can use the following kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement
(a) Let's assume that the initial velocity, u, is 0 cm/s, since the blood starts from rest. The final velocity, v, is +26 cm/s, and the displacement, s, is +1.9 cm. Plugging these values into the kinematic equation, we have:
(26 cm/s)^2 = (0 cm/s)^2 + 2a * (1.9 cm)
676 cm^2/s^2 = 0 cm^2/s^2 + 3.8 a cm^2/s^2
676 cm^2/s^2 = 3.8 a cm^2/s^2
To isolate a, we divide both sides of the equation by 3.8 cm^2/s^2:
a = 676 cm^2/s^2 ÷ 3.8 cm^2/s^2
a ≈ 178.42 cm/s^2
Therefore, the acceleration of the blood is approximately 178.42 cm/s^2.
(b) To determine the time it takes for the blood to reach its final velocity, we can use the equation:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since we know the final velocity, v, is +26 cm/s and the initial velocity, u, is 0 cm/s, we can plug these values into the equation:
26 cm/s = 0 cm/s + (178.42 cm/s^2) * t
t = (26 cm/s) / (178.42 cm/s^2)
t ≈ 0.146 s
Therefore, it takes approximately 0.146 seconds for the blood to reach its final velocity.
To solve this problem, we can use the equations of motion. In particular, we can use the equation:
v^2 = u^2 + 2as
where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
(a) To find the acceleration, we are given the initial velocity (u = 0 cm/s), the displacement (s = +1.9 cm), and the final velocity (v = +26 cm/s). Plugging these values into the equation above, we can solve for the acceleration:
(+26 cm/s)^2 = (0 cm/s)^2 + 2a(+1.9 cm)
676 cm^2/s^2 = 3.8 cm * a
Simplifying the equation, we have:
a = 676 cm^2/s^2 / 3.8 cm
a ≈ 178 cm/s^2
Therefore, the acceleration of the blood is approximately 178 cm/s^2.
(b) To find the time it takes for the blood to reach its final velocity, we can use the equation:
v = u + at
Rearranging the equation to solve for time (t), we have:
t = (v - u) / a
Plugging in the values, we have:
t = (+26 cm/s - 0 cm/s) / 178 cm/s^2
Simplifying the equation, we get:
t ≈ 0.146 s
Therefore, it takes approximately 0.146 seconds for the blood to reach its final velocity.