#### 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?

#### Solutions

Verified#### Step 1

1 of 2Using 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:

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

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

#### Step 1

1 of 8The final velocity of the left ventricle of the heart is:

$v=26\,\text{cm/s}$

and the starting velocity is zero: $v_0=0\,\text{cm/s}$
**a)** If the displacement is:

$x=2.0\,\text{cm}$

we have to calculate the acceleration.
**b)** We have to calculate the time needed to reach the final velocity.