1st derivative gives velocity;
d r(t)/ dt = 2t i + 6 j + 4/t k
2nd derivative gives acceleration;
d^2 r(t)/ dt^2 = 2 i - 4/ t^2
Speed ;
Square root of (4 t^2 + 36 + 16/ t^2)
For a given time, like 2 seconds, t will be 2. And answer of speed will be scalar.
2. A dilute solution means that the amount of solvent (water, for this particular case) is significantly larger than the solute (salt). Thus, the answer is D.
6. John Dalton's atomic theory states that matter is made up of tiny indestructible objects called matter. The theory also indicates that although same elements have the same atoms, each element have unique set atoms that deinfe them. From this, we can conclude that the wrong assumption is C.
9. Atoms, by default, are electrically neutral. When an atom loses or gains electron/s, then they become ionized atoms or commonly called as ions. Thus, ionized atoms imply unequal number of protons and electrons. This means the answer must be A.
11. Analgesics are commonly used to relieve pain. Thus, the answer is C.
14. Adding up the atomic mass of the individual atoms will give you the molar mass of a compound. Therefore, the answer is B.:
15. The pH scale provides us the alkalinity or acidity of a solution based on the value. A value between 0 to 6 indicates that the solution is acidic. 7 is considered neutral and a value between 7 and 14 indicates that the solution is basic. Thus, the answer is D.
19. An element has consistent properties and can no longer be further identified into having individual properties. Thus, the answer is A.
20. The valence of an element dependeds on the number of electrons on the outermost shell. Thus, it is equal to the number of charge negative or positive charges on the ion. Hence, we have A<span>.
:</span>
Answer:
W = 2352 J
Explanation:
Given that:
- mass of the bucket, M = 10 kg
- velocity of pulling the bucket, v = 3
- height of the platform, h = 30 m
- rate of loss of water-mass, m =
Here, according to the given situation the bucket moves at the rate,
The mass varies with the time as,
Consider the time interval between t and t + ∆t. During this time the bucket moves a distance
∆x = 3∆t meters
So, during this interval change in work done,
∆W = m.g∆x
<u>For work calculation:</u>
![W=\int_{0}^{10} [(10-0.4t).g\times 3] dt](https://tex.z-dn.net/?f=W%3D%5Cint_%7B0%7D%5E%7B10%7D%20%5B%2810-0.4t%29.g%5Ctimes%203%5D%20dt)
![W= 3\times 9.8\times [10t-\frac{0.4t^{2}}{2}]^{10}_{0}](https://tex.z-dn.net/?f=W%3D%203%5Ctimes%209.8%5Ctimes%20%5B10t-%5Cfrac%7B0.4t%5E%7B2%7D%7D%7B2%7D%5D%5E%7B10%7D_%7B0%7D)
Answer:
α = 395 rad/s²
Explanation:
Main features of uniformly accelerated circular motion
A body performs a uniformly accelerated circular motion when its trajectory is a circle and its angular acceleration is constant (α = cte). In it the velocity vector is tangent at each point to the trajectory and, in addition, its magnitude varies uniformly.
There is tangential acceleration (at) and is constant.
at = α*R Formula (1)
where
α is the angular acceleration
R is the radius of the circular path
There is normal or centripetal acceleration that determines the change in direction of the velocity vector.
Data
R = 0.0600 m :blade radius
at = 23.7 m/s² : tangential acceleration of the blades
Angular acceleration of the blades (α)
We replace data in the formula (1)
at = α*R
23.7 = α*(0.06)
α = (23.7) / (0.06)
α = 395 rad/s²
The presence of potential energy between particles supports the shape of a heating curve.
<h2>Potential energy and heating curve</h2>
The existence of potential energy between particles supports the shape of a heating curve because potential energy causes the heating curve flat as well as in curve form. The heating curves show how the temperature changes as a substance is heated up.
The potential energy of the molecules will increase anytime energy is being supplied to the system but the temperature is not increasing so when the heating curve go flat it means there is potential energy so we can conclude that the existence of potential energy between particles supports the shape of a heating curve.
Learn more about heating curve here: brainly.com/question/11991469
Learn more: brainly.com/question/26153233
