Applications of the Equations of Kinematics

[amiemgm]

Homework Statement

Please help me with this problem. If you could at least give me the formula I could probably figure it out. I have worked out all of my homework but this one.

Please type out the formula in word form. I have a hard time figuring out what is squared and what all is under the division symbol, ex. (x= v^2 - vo^2 / 2a) displacement equals (final velocity squared minus initial velocity squared) divided by (2 times acceleration). Thanks I greatly appreciate it.

Question:
The left ventricle of the heart accelerates blood from rest to a velocity of +27 cm/s.

(a) If the displacement of the blood during the acceleration is +1.9 cm, determine its acceleration (in cm/s2).

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

Homework Equations

The Attempt at a Solution

 

[Texag]

Work Energy theorem. Work done equals energy. (Force)x(Distance)= 1/2 (mass)(velocity)^2.

Take mass out of each side of the equation. You have this written already, just apply it.

Under constant acceleration, Velocity equals acceleration x time.

 

[amiemgm]

Thanks,

I got 192 cm/s^2 for answer to A. And 14 s for answer to B. Seems like they would have asked for time first since I used it to figure out the acceleration.

Thanks again

 

[Tmcm531]

Actually, the time should be 0.14 s, I'm pretty sure. Here is the equation I used to calculate time: v = vo + at (final velocity is equal to initial velocity plus acceleration times time). Therefore, t = v - vo/a, which yields 0.14 s.

 

[rwisz]

The equations of kinematics are essential in solving problems involving motion, such as the one presented in this question. To solve this problem, we can use the equation for displacement, which is given as:

x = xo + vot + 1/2at^2

Where:
x = displacement
xo = initial displacement (in this case, 0)
vo = initial velocity (in this case, 0)
a = acceleration
t = time

We can also use the equation for final velocity, which is given as:

v = vo + at

Where:
v = final velocity
vo = initial velocity (in this case, 0)
a = acceleration
t = time

(a) To determine the acceleration of the blood, we can use the first equation and substitute the given values:

1.9 cm = 0 + (0)(t) + 1/2(a)(t^2)

Solving for a, we get:
a = (2*1.9 cm)/(t^2) = 3.8/t^2

(b) To determine the time it takes for the blood to reach its final velocity, we can use the second equation and substitute the given values:

27 cm/s = 0 + a(t)

Substituting the value of a from part (a), we get:
27 cm/s = 3.8/t^2 * t

Solving for t, we get:
t = √(27/3.8) = 2.32 seconds

Therefore, it takes the blood 2.32 seconds to reach its final velocity of +27 cm/s.