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3 years ago

Explain what exponential growth is?

1 answer:

6 0

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

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Find the net work W done on the particle by the external forces during the motion of the particle in terms of the initial and fi

steposvetlana [31]

Answer:

$W=K_f-K_i$

Explanation:

The work done on a particle by external forces is defined as:

$W=\int\limits^{r_f}_{r_i} {F\cdot dr} \,$

According to Newton's second law $F=ma$ . Thus:

$W=\int\limits^{r_f}_{r_i}{ma\cdot dr} \,\\$

Acceleration is defined as the derivative of the speed with respect to time:

$W=m\int\limits^{r_f}_{r_i}{\frac{dv}{dt}\cdot dr} \,\\\\W=m\int\limits^{r_f}_{r_i}{dv \cdot \frac{dr}{dt}} \,$

Speed is defined as the derivative of the position with respect to time:

$W=m\int\limits^{v_f}_{v_i} v \cdot dv \,$

Kinetic energy is defined as $K=\frac{mv^2}{2}$ :

$W=m\frac{v_f^2}{2}-m\frac{v_i^2}{2}\\W=K_f-K_i$

3 0

3 years ago

What is the volume of an object that has a density of 65g/cm3 and a mass of 130g.

lora16 [44]

Density ρ is mass m per unit volume v, or

ρ = m / v

Solving for v gives

v = m / ρ

So the given object has a volume of

v = (130 g) / (65 g/cm³) = 2 cm³

5 0

3 years ago

The displacement of a car is a function of time as follows: x(t)=25+3.0t², with x is in meters. Find the average velocity betwee

aniked [119]

Answer: 15m/s

Explanation: Average Velocity is vector describing the total displacement of an object and the time taken to change its position. It is represented as:

$v=\frac{\Delta x}{\Delta t}$

At t₁ = 1.0s, displacement x₁ is:

$x(1)=25+3(1)^{2}$

x(1) = 28

At t₂ = 4.0s:

$x(4)=25+3(4)^{2}$

x(4) = 73

Then, average speed is

$v=\frac{73-28}{4-1}$

v = 15

The average velocity of a car between t₁ = 1s and t₂ = 4s is 15m/s

5 0

3 years ago

What happens to the density if the volume of an object decrease and the mass remains the same?

vekshin1

The density would increase because you still have the same amount of weight, but it is just packed more tightly in a smaller object.

7 0

3 years ago

Suppose you have three identical metal spheres, AA, BB, and CC. Initially sphere AA carries a charge qq and the others are uncha

Sedaia [141]

Complete Question

Suppose you have three identical metal spheres, A, B, and C. Initially sphere A carries a charge q and the others are uncharged. Sphere A is brought in contact with sphere B, and then the two are separated. Spheres CC and BB are then brought in contact and separated. Finally spheres AA and CC are brought in contact and then separated. What is the final charge on the sphere B, in terms of q?

a. 3/8q

b. 1/4q

c. 3/4q

d. q

e. 5/8q

f. 1/3q

g.1/2q

h. 0

Answer:

The correct option is b

Explanation:

From the question we are told that

The charge carried by A is q C

The charge carried by B is 0 C

The charge carried by C is 0 C

When A and B are brought close and then separated the charge carried by A and B is mathematically evaluated as

$\frac{ 0 + q}{2} = \frac{q}{2}$

When C and B are brought close and then separated the charge carried by C and B is mathematically evaluated as

$\frac{0 + \frac{q}{2} }{2} = \frac{q}{4}$

When C and A are brought close and then separated the charge carried by C and A is mathematically evaluated as

$\frac{\frac{q}{4} + \frac{q}{2} }{2} = \frac{3q}{8}$

Looking at these calculation we can see that the charge carried by B is

$\frac{q}{4} C$

8 0

3 years ago