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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Classify each possible hypothesis about a medicinal aloe vera plant as falsifiable or non-falsifiable.

pychu [463]

Answer:

Aloe vera is a succulent plant species ( with fleshy water storing tissue) belonging to the genus Aloe.

It is used in many products ( including beverages, cosmetic products as gel, medicinal ointments). Its juice is quite bitter in taste. It is known to be the best skin moisturizer and can be used for healing wounds by enhancing the renewal of damaged cells. It is also used as an anticarcinogen, thus reduces the chances of cancer.

Thus, the given hypothesis can be classified as falsifiable ( which is proven wrong) or non-falsifiable ( which is proven right) in the following way-

Falsifiable-

Aloe vera juice tastes better than carrot juice.

Non Falsifiable-

Aloe vera gel is the best natural skin moisturizer.

Aloe vera gel can heal wounds by boosting cell renewal.

Drinking aloe juice can reduce the risk of lung cancer.

7 0

4 years ago

A car with a mass of 1380 Kg is traveling at 23 m/s to the north. A truck with a mass of 1625 Kg is traveling at 26 m/s to the s

trasher [3.6K]

Answer: -3.49 m/s (to the south)

Explanation:

This problem can be solved by the Conservation of Momentum principle which establishes the initial momentum $p_{i}$ must be equal to the final momentum $p_{f}$ , and taking into account this is aninelastic collision: