The left ventricle of the heart accelerates blood from the rest to a velocity of +24.2 cm/s. (a) if the displacement of the blood during the acceleration is +1.73 cm, determine its acceleration ( in cm/s2). (b) how much time does blood take to reach its final velocity?
(a) We can use the formula for acceleration:
acceleration = (final velocity - initial velocity) / time
Since the initial velocity is 0 (rest), the formula becomes:
acceleration = (final velocity - 0) / time
acceleration = final velocity / time
We are given the final velocity as +24.2 cm/s and displacement as +1.73 cm. We can use the formula for displacement to calculate time:
displacement = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the initial velocity is 0, the formula becomes:
displacement = 0.5 * acceleration * time^2
1.73 cm = 0.5 * acceleration * time^2
Substituting the value of acceleration from the first formula:
1.73 cm = 0.5 * (24.2 cm/s / time) * time^2
1.73 cm = 12.1 cm/s * time
Solving for time:
time = 1.73 cm / 12.1 cm/s
time ≈ 0.143 s
Now we can substitute this value of time back into the first formula to solve for acceleration:
acceleration = 24.2 cm/s / 0.143 s
acceleration ≈ 169.23 cm/s^2
Therefore, the acceleration of the blood is approximately 169.23 cm/s^2.
(b) To find the time it takes for the blood to reach its final velocity, we can use the same formula:
acceleration = (final velocity - initial velocity) / time
Solving for time:
time = (final velocity - initial velocity) / acceleration
time = (24.2 cm/s - 0) / 169.23 cm/s^2
time ≈ 0.143 s
Therefore, the blood takes approximately 0.143 s to reach its final velocity.