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fredd
3 months ago
10

The position of a particle is r⃗ (t)=(3.0t2iˆ+5.0jˆ−6.0tkˆ)m. (a) Determine its velocity and acceleration as functions of time.

(b) What are its velocity and acceleration at time t = 0?
Physics
1 answer:
ValentinkaMS [3.4K]3 months ago
8 0

Explanation:

It is stated that,

The position of a particle is defined by:

r(t)=(3t^2i+5j-6tk)\ m

(a) The velocity of a particle can be expressed as:

v=\dfrac{dr(t)}{dt}

Substituting the values,

v=\dfrac{d}{dt}(3t^2+5-6t)\\\\v=(6ti-6k)\ m/s

The acceleration of the particle can be expressed as:

a=\dfrac{dv}{dt}\\\\a=\dfrac{d}{dt}(6t-6)\\\\a=6i\ m/s^2

(b) At time t = 0,

Velocity, v = 6k m/s

Acceleration, a = 6i m/s²

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Consider an electron with charge −e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e.
kicyunya [3294]

Result:

v=\sqrt{k\frac{e^2}{m_e r}}, 2.18\cdot 10^6 m/s

Explanation:

The electromagnetic attraction between the electron and the proton in the nucleus is equivalent to the centripetal force:

k\frac{(e)(e)}{r^2}=m_e \frac{v^2}{r}

where

k represents the Coulomb constant

e denotes the charge of the electron

e denotes the charge of the proton in the nucleus

r signifies the distance from the electron to the nucleus

v indicates the velocity of the electron

is the mass of the electron

Rearranging for v, we determine

v=\sqrt{k\frac{e^2}{m_e r}}

Inside a hydrogen atom, the distance separating the electron from the nucleus is roughly

r=5.3\cdot 10^{-11}m

while the mass of the electron is

m_e = 9.11\cdot 10^{-31}kg

and the charge is

e=1.6\cdot 10^{-19} C

By plugging in the values into the formula, we achieve

v=\sqrt{(9\cdot 10^9 m/s) \frac{(1.6\cdot 10^{-19} C)^2}{(9.11\cdot 10^{-31} kg)(5.3\cdot 10^{-11} m)}}=2.18\cdot 10^6 m/s

7 0
2 months ago
Two charges q1 = 5 µC, q2 = -26 µC, are L = 19 cm apart. A third charge is to be placed on the line between the two charges. How
Keith_Richards [3271]
The electric force between two objects is expressed as being proportional to the product of their charges and inversely proportional to the square of the distance separating them. In this instance, the distance between the first two charges is 19 cm. We formulate the equation k q1 q3/ (x)^2 = k q2 q3/ (19-x)^2, where x denotes the separation between q1 and q3. The charge q3 cancels out, and q2 is used in absolute terms. The resulting value of x is 5.79 cm.
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2 months ago
Which model is used to describe the interaction of external forces that affect an organization's strategy and ability to compete
ValentinkaMS [3465]

Answer:

Competitive forces model

Explanation:

The Competitive forces model is a crucial instrument in strategic analysis aiming to assess an organization’s competitiveness. Commonly referred to as the "Five Force Model of Porter", this framework includes five key factors: the intensity of rivalry among existing competitors, the negotiating power of buyers, the threat posed by potential new entrants, the bargaining strength of suppliers, and the risk of substitute products or services.

These elements significantly influence an organization's competitive strategy and its likelihood of success.

5 0
3 months ago
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