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3 years ago

How do I prove that a = v * dv/dx?

1 answer:

6 0

Your book has applied the chain rule to produce:
dv/dt = dv/dx * dx/dt
Now, we can get dv/dx by:
1) Differentiate
x = vt, with respect to v.
dx/dv = t
Now, if we take the inverse of this, we can obtain dv/dx
dv/dx = 1/t
This is also proven by the fact that dv/dx is the change in velocity and if you multiply it by dv/dx, which is equivalent to dividing by the change in time, as we just proved, then you obtain acceleration.

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Why do most amphibians return to the water to reproduce?

Ymorist [56]

C. amphibian eggs do not contain a protective shell

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2 years ago

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A body with initial velocity 8.0 m/s moves along a straight line with constant acceleration and travels

Aleksandr [31]

Answer:

(a) The average velocity is 16 m/s

(b) The acceleration is 0.4 m/s^2

(c) The final velocity is 24 m/s

Explanation:

Constant Acceleration Motion

It's a type of motion in which the velocity (or the speed) of an object changes by an equal amount in every equal period of time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, final speed is calculated as follows:

$v_f=v_o+at\qquad\qquad [1]$

The distance traveled by the object is given by:

$\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2]$

(a) The average velocity is defined as the total distance traveled divided by the time taken to travel that distance.

We know the distance is x=640 m and the time taken t= 40 s, thus:

$\displaystyle \bar v=\frac{x}{t}=\frac{640}{40}=16$

The average velocity is 16 m/s

Using the equation [1] we can solve for a:

$\displaystyle a=\frac{v_f-v_o}{t}$

$\displaystyle a= 2\frac{x-v_ot}{t^2}$

Since vo=8 m/s, x=640 m, t=40 s:

$\displaystyle a= 2\frac{640-8\cdot 40}{40^2}=0.4$

The acceleration is 0.4 m/s^2

(b) The final velocity is calculated by [1]:

$v_f=8+0.4\cdot 40$

$v_f=8+16=24$

The final velocity is 24 m/s

3 0

3 years ago

Heat is added to an open pan of water at 100.0°c, vaporizing the water. the expanding steam that results does 43.0 kj of work, a

vampirchik [111]

Heat = change in internal energy + Work done The internal energy of a system = heat added and mechanical work done by the system, i.e. U = Q + W rearranging the formula above, will give us: Q = deltaU + W
Q = U - W = 604 kJ - 43.0 kJ = 561,000 J would be the answer.

6 0

3 years ago

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Consider a string with a length of (47.5 A) cm tied at both end (like on a stringed instrument). If the frequency of the first h

zubka84 [21]

To solve this problem it is necessary to apply the concepts related to wavelength as a function of frequency and speed, as well as to determine the wavelength as a function of length.

From the harmonic vibration generated we know that the total length of the string will be equivalent to a half of the wavelength, that is

$L = \frac{\lambda}{2} \rightarrow \lambda = 2L$

Where,

$\lambda =$ Wavelength

Therefore the wavelength for us would be,

$\lambda = 2*47.5cm = 95cm = 0.95m$

From the relationship of speed, frequency and wavelength we know that

$\lambda = \frac{v}{f} \rightarrow v = \lambda f$

$v = (0.95m)(245Hz)$

$v = 232.75 m/s$

Therefore the speed of the wave is 232.75m/s

4 0

3 years ago

What's needed to know

Diano4ka-milaya [45]

You're a little late. But if you want some short, quick rules, then these are
a couple that I would take in with me (stored only in my brain, of course):

-- If something is not accelerating or moving at all, then all the forces on it
must add up to zero. That could even mean a hanging rope.

-- In a vertical rope, the tension in it is the same everywhere in the rope.
The tension is the weight of whatever is hanging from the bottom.

That's really all I'm sure of, based on your hazy, fuzzy description of
what you've been doing in class. I don't want to get into things that
you might not have learned yet, and confuse you.

8 0

3 years ago

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