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Firlakuza [10]
3 years ago
12

A particle initially at rest moves along in a line so that its acceleration is a(t) = 10/(t+1) for t>=0.

Physics
1 answer:
ddd [48]3 years ago
4 0

Answer: 16.09m/s

Explanation:

Given the acceleration a(t) = 10/(t+1), to derive the velocity function, we need integrate the acceleration function.

v(t) = integral{10/t+1}dt

Since all constants always come out of the integral, the equation becomes;

v(t) = 10integral{1/t+1}dt

One of the integral law is that if the numerator of the function to be integrated is the differential of the denominator, the resulting answer will be natural logarithm of the denominator i.e ln(t+1) since the denominator is ln(t+1) and if differentiated will give us 1 which is the numerator hence, the reason for the answer ln(t+1)

v(t) = 10ln(t+1)

@ t= 4, the velocity of the particle

v(4) = 10ln(4+1)

v(4) = 10ln5

v(4) = 16.09m/s²

Therefore, the velocity of the particle at time t=4 is 16.09m/s

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7 0
3 years ago
The bob (weight) at the end of a pendulum has a mass of 0.3 kilograms. The bob is pulled to position B and allowed to swing. It
Ivahew [28]

Answer:

0.147 J

Explanation:

The total energy that has been transformed into thermal energy is equal to the loss of gravitational potential energy between the initial situation (bob at h=0.5 m above the ground) and the final situation (bob back but at h=0.45 m above the ground).

Therefore, we have

E_{thermal}=\Delta U=mgh_1 - mgh_2 = mg(h_1 -h_2)

where

m = 0.3 kg is the mass of the bob

g = 9.8 m/s^2

h1 = 0.5 m is the initial height

h2 = 0.45 m is the final height

Substituting, we find the thermal energy

E_{thermal}=(0.3 kg)(9.8 m/s^2)(0.5 m-0.45 m)=0.147 J

Therefore, the energy transformed into thermal energy is 0.147 J.

3 0
3 years ago
A body of mass 3.0kg moves with a velocity 10 m/s. calculate the momentum of the body​
Aleksandr-060686 [28]
P=30 kg•m/s. This will be your correct answer.
4 0
2 years ago
5. A helicopter scoops a load of water out of a lake, to dump on a forest fire. The helicopter exerts 6480
Strike441 [17]

Answer:

h = 250 m

Explanation:

Given that,

The helicopter exerts 6480  N of force on the water while rising high enough to fly over a mountain.

The helicopter does 1.62\times 10^6\ J of work on the water lifting it.

We need to find how high does it lift the water. Work done is given by :

W=Fh\\\\h=\dfrac{W}{F}\\\\h=\dfrac{1.62\times 10^6}{6480}\\\\h=250\ m

So, it can lift the water to a height of 250 m.

6 0
3 years ago
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balu736 [363]

Answer:

Explanation:

String theory proposes that the fundamental constituents of the universe are one-dimensional “strings” rather than point-like particles. String theory also requires six or seven extra dimensions of space, and it contains ways of relating large extra dimensions to small ones. In statistical mechanics, entropy is an extensive property of a thermodynamic system. It quantifies the number Ω of microscopic configurations that are consistent with the macroscopic quantities that characterize the system theyre related  It later developed into superstring theory, which posits a connection called supersymmetry between bosons and the class of particles called fermions. Five consistent versions of superstring theory were developed before it was conjectured in the mid-1990s that they were all different limiting cases of a single theory in 11 dimensions known as M-theory. In late 1997, theorists discovered an important relationship called the AdS/CFT correspondence, which relates string theory to another type of physical theory called a quantum field theory.

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