Question

Blood is accelerated from rest to 30.0 cm/s in a distance of 1.80 cm by the left ventricle of the heart. (a) Make a sketch of the situation. (b) List the knowns in this problem. (c) How long does the acceleration take? To solve this part, first identify the unknown, and then discuss how you chose the appropriate equation to solve for it. After choosing the equation, show your steps in solving for the unknown, checking your units. (d) Is the answer reasonable when compared with the time for a heartbeat?

Answer 1

Answer:

a. Picture attached

b. V, X

c. $t=0.12 s$

d. It makes sense cosidering that a normal heart beat rate is between 60 and 100 beats per minute (bpm).

Explanation:

First we have to identify the unknown of this problem:

$a: acceleration\\t: time$

Considering the characteristics of the problem and that distance and velocity are specified, the acceleration is constant, for that reason we use the equations of uniformly accelerated motion as follows:

$v=v_{0}+at\\ x=x_{0}+ v_{0}+\frac{1}{2}at^{2}$

If we reorganize the equations, considering that $x_{0}$ and $v_{0}$ are zero because motion starts from rest , we have:

$a=\frac{v}{t} \\x=\frac{1}{2}at^{2}  =\frac{1}{2}\frac{v}{t} t^{2}=\frac{1}{2} vt\\t=\frac{2x}{v} \\t=\frac{2*1.80cm}{30.0\frac{cm}{s} } \\t=0.12 s$

Finally, the analysis of the result leaves us to understand why the normal heart beat rate varies between 60 and 100 bpm.