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A human heart pumps 60 mL of blood into the aorta in a 0.1 s stroke, accelerating blood from rest to 50 cm/s. What is the average acceleration of the blood?

Answer

The average acceleration is the change in velocity divided by the time: $a_{avg}=\Delta v/\Delta t$. Converting $50\,\text{cm/s}=0.50\,\text{m/s}$ and using $\Delta t=0.1\,\text{s}$, $$a_{avg}=\frac{0.50-0}{0.1}=5\,\text{m/s}^2.$$

Explanation

What the problem is asking

You are given how fast the blood ends up moving and how long the heart takes to do that in one stroke. Average acceleration depends only on the velocity change and the time interval, not on the volume pumped.

Convert the final speed to SI units

Physics acceleration is usually reported in $\text{m/s}^2$, so convert:

$$50\,\text{cm/s}=\frac{50}{100}\,\text{m/s}=0.50\,\text{m/s}$$

Use the average-acceleration formula

Starting from rest means $v_i=0$. With $v_f=0.50\,\text{m/s}$ and $\Delta t=0.1\,\text{s}$:

$$a_{avg}=\frac{\Delta v}{\Delta t}=\frac{v_f-v_i}{\Delta t}=\frac{0.50-0}{0.1}=5\,\text{m/s}^2$$

Quick reasonableness check

A $0.50\,\text{m/s}$ speed increase in just $0.1\,\text{s}$ is a fairly quick ramp-up, so an acceleration of a few $\text{m/s}^2$ makes sense; here it is $5\,\text{m/s}^2$.

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