Question

the human circulatory system is closed - that is, the blood pumped out of the left ventricle of the heart into the arteries is constrained to a series of continuous, branching vessels as it passes through the capillaries and then into the veins as it returns to the heart. the blood in each of the heart’s four chambers comes briefly to rest before it is ejected by contraction of the heart muscle. the contraction of the left ventricle lasts 250 ms and the speed of blood flow in the aorta (the large artery leaving the heart) is 0.80 m/s at the end of the contraction. what is the average acceleration of a red blood cell as it leaves the heart? options: 310 m/s², 31 m/s², 3.2 m/s², 0.32 m/s²

Explanation:

Step1: Identify initial and final velocity, time

Assume initial velocity \( u = 0 \, \text{m/s} \) (starts from rest), final velocity \( v = 0.80 \, \text{m/s} \), time \( t = 250 \, \text{ms} = 250 \times 10^{-3} \, \text{s} = 0.25 \, \text{s} \).

Step2: Use acceleration formula \( a=\frac{v - u}{t} \)

Substitute values: \( a=\frac{0.80 - 0}{0.25} \).

Step3: Calculate acceleration

\( a=\frac{0.80}{0.25}=3.2 \, \text{m/s}^2 \)? Wait, no, wait the options have 310, 31, 3.2, 0.32. Wait, maybe I misread the final velocity? Wait, no, the problem says "speed of blood flow in the aorta is 0.80 m/s at the end of the contraction". Wait, maybe initial velocity is not zero? Wait, no, during contraction, the blood is accelerated from rest? Wait, maybe the time is 250 ms = 0.25 s. Wait, let's recalculate: \( a=\frac{v - u}{t} \). If \( u = 0 \), \( v = 0.80 \, \text{m/s} \), \( t = 0.25 \, \text{s} \), then \( a = 3.2 \, \text{m/s}^2 \)? But the options have 310, 31, 3.2, 0.32. Wait, maybe the time is 250 ms is 0.25 s, but maybe the final velocity is 0.80 m/s, but maybe I made a mistake. Wait, no, let's check the options. Wait, the correct calculation: \( a=\frac{\Delta v}{\Delta t}=\frac{0.80 - 0}{250 \times 10^{-3}}=\frac{0.80}{0.25}=3.2 \, \text{m/s}^2 \)? But the options have 3.2 m/s² as an option? Wait, the options are: 310 m/s², 31 m/s², 3.2 m/s², 0.32 m/s². So the correct answer should be 3.2 m/s²? Wait, no, wait maybe the initial velocity is not zero. Wait, maybe the blood is moving before contraction? No, the contraction ejects the blood, so initial velocity during contraction is 0. So acceleration is \( \frac{0.80}{0.25}=3.2 \, \text{m/s}^2 \).

Answer:

3.2 m/s² (corresponding to the option with 3.2 m/s²)