#### Question

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 +2. 0 cm, determine its acceleration

$\left( \text { in } \mathrm { cm } / \mathrm { s } ^ { 2 } \right)$

(b) How much time does blood take to reach its final velocity?

Verified

#### Step 1

1 of 2

Using the following equation of motion:

$v^2=v_0^2+2ax$

we can get the acceleration as:

\begin{align}a=\dfrac{v^2-v_0^2}{2x}\end{align}

$\textbf{(a)}$ Assume we have left ventricle of the heart, which accelerates blood from rest $v_0=0$ to a speed of $v=26 \mathrm{~cm\cdot s^{-1}}$, if the displacement of the blood is $x=2$ cm, the acceleration is therefore:

\begin{align*}a&=\dfrac{(26 \mathrm{~cm\cdot s^{-1}})^2-0}{2(2 \mathrm{~cm})}\\ &=169 \mathrm{~cm\cdot s^{-1}} \end{align*}

$\boxed{a=169 \mathrm{~cm\cdot s^{-1}}}$

$\textbf{(b)}$ Using the following equation of motion:

$v=v_0+at$

we can get the time as:

\begin{align*}t&=\dfrac{v-v_0}{a}\\ &=\dfrac{(26 \mathrm{~cm\cdot s^{-1}})-0}{(169 \mathrm{~cm\cdot s^{-1}})}\\ &=0.154 \mathrm{~s} \end{align*}

$\boxed{t=0.154 \mathrm{~s}}$

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