Chapter 2: Q. 10 (page 59)

FIGURE EX2.7 showed the velocity graph of blood in the aorta. What is the blood’s acceleration during each phase of the motion, speeding up and slowing down?

Expert verified

The acceleration of blood during the speeding up phase is $16 m s^{- 2}$ .

The acceleration of blood during the speeding down phase is $- 5.3 m s^{- 2}$ .

Step by step solution

The velocity-time graph of blood in the aorta is shown below

Average acceleration is given by the slope of the velocity-versus-time graph.

For the first phase, consider two points $(t_{1}, v_{1}) = (0.1, 0)$ and $(t_{2}, v_{2}) = (0.15, 0.8)$ .

The acceleration of the blood is

$a = \frac{v_{2} - v_{1}}{t_{2} - t_{1}} = \frac{0.8 - 0}{0.15 - 0.1} = 16 \frac{m}{s^{2}}$

Therefore, the acceleration of blood during the speeding up phase is $16 \frac{m}{s^{2}}$ .

For the second phase, consider two points $(t_{2}, v_{2}) = (0.15, 0.8)$ and $(t_{3}, v_{3}) = (0.3, 0)$ .

The acceleration of the blood is

$a = \frac{v_{3} - v_{2}}{t_{3} - t_{2}} = \frac{0 - 0.8}{0.3 - 0.15} = - 5.3 \frac{m}{s^{2}}$

Therefore, the acceleration of blood during the speeding down phase is $- 5.3 \frac{m}{s^{2}}$ .

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