# Math Help - acceleration, velocity problem

1. ## acceleration, velocity problem

The left ventricle of the heart accelerates blood from rest to a velocity of +22 cm/s.
(a) If the displacement of the blood during the acceleration is +2.1 cm, determine its acceleration (in cm/s2).
should be in cm/s2

(b) How much time does it take for the blood to reach its final velocity?
in seconds?

thankyou for looking at this.

2. Originally Posted by rcmango
The left ventricle of the heart accelerates blood from rest to a velocity of +22 cm/s.
(a) If the displacement of the blood during the acceleration is +2.1 cm, determine its acceleration (in cm/s2).
should be in cm/s2

(b) How much time does it take for the blood to reach its final velocity?
in seconds?

thankyou for looking at this.
We have unknown acceleration $a$ acting for unknown time $t$. Then:

$
v(t)=at
$

as the blood starts from rest, and displacement:

$
s(t)=at^2/2
$

hence substituting in the given final velocity and displacements we have:

$
22=at
$

and

$
2.1=at^2
$

Now you solve this pair of quations for $a$ and $t$ to answer the question

RonL

3. Originally Posted by rcmango
The left ventricle of the heart accelerates blood from rest to a velocity of +22 cm/s.
(a) If the displacement of the blood during the acceleration is +2.1 cm, determine its acceleration (in cm/s2).
should be in cm/s2

(b) How much time does it take for the blood to reach its final velocity?
in seconds?

thankyou for looking at this.
The acceleration is constant.

Given:
Vo = 0
V final, Vf = 22 cm/sec
distance travelled, d = 2.1 cm

d = [(Vo +Vf)/2]*t
2.1 = [(0 +22)/2]*t
2.1 =11t
t = 2.1/11 = 0.191 sec -------------answer.

Vf = Vo +at
22 = 0 +a(0.191)
a = 22/0.191 = 115.2 cm/sdec/sec -------------answer.

4. Originally Posted by rcmango
The left ventricle of the heart accelerates blood from rest to a velocity of +22 cm/s.
(a) If the displacement of the blood during the acceleration is +2.1 cm, determine its acceleration (in cm/s2).
should be in cm/s2

(b) How much time does it take for the blood to reach its final velocity?
in seconds?

thankyou for looking at this.
Actually, you can get the answer to part a) directly if you use
$v^2 = v_0^2 + 2as$

-Dan