The left ventricle of the heart accelerates blood from rest to a velocity of + 24.8 cm/s. (a) If the displacement of the blood during the acceleration is + 2.97 cm, determine its acceleration (in cm/s2). (b) How much time does blood take to reach its final velocity?
vf^2=2ad you know vf, d, solve for a.
vf=at solve for time t.
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To find the acceleration and time taken for the blood to reach its final velocity, we can use the equations of motion.
(a) To find the acceleration:
Here, we know the initial velocity (u) is 0 cm/s (as the blood is at rest), the displacement (s) is +2.97 cm, and the final velocity (v) is +24.8 cm/s.
The first equation of motion is:
v^2 = u^2 + 2as
Rearranging the equation to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
Substituting the given values, we have:
a = (24.8^2 - 0^2) / (2 * 2.97)
Calculating this, we get:
a = 62.09 cm/s^2
So, the acceleration of the blood is 62.09 cm/s^2.
(b) To find the time taken:
We can use the second equation of motion:
v = u + at
Rearranging the equation to solve for time (t):
t = (v - u) / a
Substituting the given values:
t = (24.8 - 0) / 62.09
Calculating this, we get:
t ≈ 0.399 seconds
So, it takes approximately 0.399 seconds for the blood to reach its final velocity.
To answer part (a), the acceleration of the blood is approximately 62.09 cm/s^2. In part (b), the blood takes approximately 0.399 seconds to reach its final velocity.