Bernoulli's principle is responsible for most of the lift produced by an airplane wing.

Which of the following expressions will have units of kg⋅m/s2? Select all that apply, where x is position, v is velocity, m is m

netineya [11]

Answer: $m \frac{d}{dt}v_{(t)}$

Explanation:

In the image attached with this answer are shown the given options from which only one is correct.

The correct expression is:

$m \frac{d}{dt}v_{(t)}$

Because, if we derive velocity $v_{t}$ with respect to time $t$ we will have acceleration $a$ , hence:

$m \frac{d}{dt}v_{(t)}=m.a$

Where $m$ is the mass with units of kilograms ( $kg$ ) and $a$ with units of meter per square seconds $\frac{m}{s}^{2}$ , having as a result $kg\frac{m}{s}^{2}$

The other expressions are incorrect, let’s prove it:

$\frac{m}{2} \frac{d}{dx}{(v_{(x)})}^{2}=\frac{m}{2} 2v_{(x)}^{2-1}=mv_{(x)}$ This result has units of $kg\frac{m}{s}$

$m\frac{d}{dt}a_{(t)}=ma_{(t)}^{1-1}=m$ This result has units of $kg$

$m\int x_{(t)} dt= m \frac{{(x_{(t)})}^{1+1}}{1+1}+C=m\frac{{(x_{(t)})}^{2}}{2}+C$ This result has units of $kgm^{2}$ and $C$ is a constant

$m\frac{d}{dt}x_{(t)}=mx_{(t)}^{1-1}=m$ This result has units of $kg$

$m\frac{d}{dt}v_{(t)}=mv_{(t)}^{1-1}=m$ This result has units of $kg$

$\frac{m}{2}\int {(v_{(t)})}^{2} dt= \frac{m}{2} \frac{{(v_{(t)})}^{2+1}}{2+1}+C=\frac{m}{6} {(v_{(t)})}^{3}+C$ This result has units of $kg \frac{m^{3}}{s^{3}}$ and $C$ is a constant

$m\int a_{(t)} dt= \frac{m {a_{(t)}}^{2}}{2}+C$ This result has units of $kg \frac{m^{2}}{s^{4}}$ and $C$ is a constant

$\frac{m}{2} \frac{d}{dt}{(v_{(x)})}^{2}=0$ because $v_{(x)}$ is a constant in this derivation respect to $t$

$m\int v_{(t)} dt= \frac{m {v_{(t)}}^{2}}{2}+C$ This result has units of $kg \frac{m^{2}}{s^{2}}$ and $C$ is a constant

6 0

3 years ago

A squirrel drops an acorn from a tree. Starting from rest, it reaches the ground 22.0 meters

Llana [10]

Does it not tell you how long it took it to reach the ground? Constant Velocity should be distance over time

7 0

3 years ago

During a blackout, you are trapped in a tall building. you want to call rescuers on your cell phone, but you can't remember whic

Gennadij [26K]

Let the height where we are trapped is H

now to find the time to reach the key at the bottom is given as

$y = v_i t + \frac{1}{2}at^2$

now we have

$H = \frac{1}{2}gt^2$

$t = \sqrt{\frac{2H}{g}}$

now if the speed of sound is considered to be 340 m/s then time taken by the sound to reach at the top is given as

$t = \frac{H}{340}$

now the total time is given as

$\sqrt{\frac{2H}{g}} + \frac{H}{340} = 3.27$

now by solving above equation we have

H = 48 m

now height of one floor is 3 m

so our position must be

$N = \frac{48}{3} = 16 th \:floor$

3 0

3 years ago

How does the Sun's gravity influence tides?

nevsk [136]

Answer: <em>Around each new moon and full moon, the sun, Earth, and moon arrange themselves more or less along a line in space. Then the pull on the tides increases, because the gravity of the sun reinforces the moon's gravity. ... This is the spring tide: the highest (and lowest) tide. Spring tides are not named for the season.</em>

8 0

3 years ago

A major physical disability usually leaves people ________ than able-bodied people with depression. Most patients "locked in" a

Ierofanga [76]

Answer:

happier; do not

Explanation:

A major physical disability usually leaves people __happier______ than able-bodied people with depression. Most patients "locked-in" a motionless body ____do not____ indicate they want to die.

4 0

3 years ago

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