Main idea force and motion

The time it takes the vehicle to reach a velocity of 48 km/h, t₁ = 20 s

The time the vehicle moves with a constant speed, t₂ = 30 s

The time it takes the vehicle to decelerate and stop, t₃ = 10 s

The acceleration of the vehicle is 0.66 m/s².

The distance the vehicle travels with constant velocity is 400 m.

The given parameters:

The total distance traveled by the vehicle is calculated as follows;

\(s_t = s_1 + s_2 + s_3\\\\s_t= ( \frac{1}{2} bh ) + (bh)+( \frac{1}{2} bh)\\\\s_t = (\frac{1}{2} t_1v_1)+ (t_2v_2)+ (\frac{1}{2} t_3v_3)\\\\600 = (0.5t_1\times 13.33) + (t_2\times 13.33) + (0.5 \times t_3 \times 13.33)\\\\600 = 6.67t_1 + 13.33t_2 + 6.67t_3 \\\\600 = 6.67(t_1 + t_3) + 13.33t_2 \ --- (1) \\\\\)

\(t_1 + t_2 + t_3 = 60\\\\t_1 + t_3 = 60 -t_2\)

\(600 = 6.67(60-t_2) + 13.33t_2\\\\600 = 400.2 - 6.67t_2 + 13.33t_2\\\\600 = 400.2 + 6.67t_2\\\\199.8 = 6.67t_2\\\\t_2 = \frac{199.8}{6.67} \\\\t_2 = 29.96 \ s\)

\(t_1 = 60-t_2 -t_3\\\\t_1 = 60 -29.96 - t_3\\\\t_1 = 30.04 -t_3\)

The acceleration of the vehicle;

\(a = \frac{v-u}{t_1} \\\\a = \frac{13.33-0}{t_1} \\\\a = \frac{13.33}{t_1}\\\\t_1 = \frac{13.33}{a}\)

The deceleration of the vehicle;

\(dec =\frac{-13.33}{t_3} \\\\|dec| = 2a\\\\\frac{13.33}{t_3} = \frac{2 (13.33)}{t_1} \\\\13.33t_1 = 2(13.33)t_3\\\\t_1 =2t_3\)

\(t_1 = 30.04 - t_3 \\\\2t_3 = 30.04 -t_3\\\\3t_3 = 30.04\\\\t_3 = \frac{30.04}{3} \\\\t_3 = 10.01 \ s\)

\(t_1 = 2t_3\\\\t_1 = 2(10.01)\\\\t_1 = 20.02 \ s\)

Thus, we can conclude the following:

The acceleration of the vehicle is calculated as follows;

\(a = \frac{13.33}{t_1} \\\\a = \frac{13.33}{20} \\\\a = 0.66 \ m/s^2\)

The distance the vehicle travels with constant velocity is calculated as;

\(s_2 = v_2 t_2\\\\s_2 = 13.33 \times 30\\\\s_2 = 400 \ m\)

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Answer:

The time is \(t = 500 \ s\)

Explanation:

From the question we are told that

  The distance of the sun from the earth is \(d = 1.5 *10^{11} \ m\)

   The speed of light is  \(c =3.0 *0^{8} \ m/s\)

Generally the time it would take is  

        \(t = \frac{d}{v}\)

=>     \(t = \frac{1.5*10^{11}}{3.0*10^{8}}\)

=>      \(t = 500 \ s\)

Answer:

5hrs

Explanation:

If 25 kg of potassium took 15 hours to decay into 3.125 kg, the half-life of potassium is 5hrs.

Answer:

6 protons

Explanation:

\(p = e = n = 6 \\  6 protons, \\ 6 neutrons, \\ and 6 electrons\)

A type of research which would be most appropriate for a research looking to see how drinking coffee impacts college students' grade point averages (GPAs) is a survey.

In Science, a research method can be defined as the scientific methods or techniques that are adopted by a researcher for the collection and analysis of data.

Generally speaking, there are different types of research method that are used for the collection of data and these include the following:

In Science, a survey simply refers to a type of research method that uses various data collection methods such as questionnaires and interviews, which favors it in revealing correlations between two data variables such as the relationship between coffee and college students' grade point averages (GPAs).

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The magnitude of the initial acceleration of the object is 4.2 m/s².

The tension in the string once the object starts moving is 13.65 N.

The magnitude of the initial acceleration of the object is calculated by applying Newton's second law of motion as follows;

F(net) = ma

m₂g - μm₁g cosθ = a(m₁ + m₂)

where;

(4.75 x 9.8) - (0.535 x 3.25 x 9.8 x cos40) = a(3.25 + 4.75)

33.5 = 8a

a = 33.5/8

a = 4.2 m/s²

The tension in the string once the object starts moving is calculated as;

T = m₁a

T = 3.25 x 4.2

T = 13.65 N

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Answer:

72m

12m x 6s=72m

there ya go

The potential energy of the roller coaster is 176,400 J (joules).

The potential energy of an object is given by the formula PE = mgh, where PE is the potential energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or vertical position of the object.

In this case, the roller coaster is at a peak of 20m and has a mass of 900kg. The acceleration due to gravity, g, is approximately 9.8 \(m/s^2\).

Using the formula, we can calculate the potential energy:

PE = mgh

= (900 kg)(9.8 \(m/s^2\))(20 m)

= 176,400 J

Therefore, the potential energy of the roller coaster is 176,400 J (joules).

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The earthquake would occur 13 minutes before 10:05 a.m. which will be at 9.52 am.

The p-waves travel with a constant velocity of 7 km/s

The time can be calculated by using the formula

t = d / v

where

T1 =  10:05 a.m

d is the distance they take to travel from the epicenter

v is the speed of the p-waves

On average, the speed of p-waves is

v = 7 km/s

d = 5600 km (given)

Substituting the values in the formula;

t = d / v

t = 5600 ÷ 7

t = 800 seconds

Converting into minutes,

t = 800 ÷ 60

t = 13.3

≈ 13 mins

T1 -  13 mins = T2

10:05 - 13 mins = 9.52 am

It means the earthquake occurred prior 13 minutes, that is at 9.52 am.

Therefore, the earthquake occurred at 9.52 am.

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Answer:

The object appears larger

Explanation:

B

We may calculate the proportion of data values that are 1.5 standard deviations or more from the mean using Chebyshev's rule in statistics. Alternately, we can calculate the proportion of data values that deviate by 2.5 standard deviations from the mean.

What does a 75% Chebyshev interval mean?

Therefore, Chebyshev's Theorem informs you that at least 75% of the values lie within the range of 100 20, or 80 to 120. In contrast, no more than 25% of cases fall outside of that range. 1.41 standard deviations is an intriguing range.

What does the Chebyshev inequality tell us?

According to Chebyshev's inequality, 75% of values are found within two standard deviations of the mean, and 88.9% are found within three standard deviations of the mean. It is true for.

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Answer:

lysosome,flagellum are the 2 structures in a cell

Answer:

a) ΔV ’= 1.66 10¹ V= 16.6 V,  b)  U = 55.64 10⁻¹² J,  c)    U_f = 1.18 10⁻¹⁰ J

d)     W = 6.236 10⁻¹¹ J

Explanation:

Capacitance can be found for a parallel plate capacitor

          C = ε₀  \(\frac{A}{d}\)  

Let's reduce the magnitudes to the SI system

           A = 9.30 cm² (1 m / 10² cm) 2 = 9.30 10⁻⁴ m²

           c = 4.50 mm (1 m / 1000 mm) = 4.50 10⁻³ m

          Co = 8.85 10⁻¹²    9.30 10⁻⁴ /4.50 10⁻³

          Co = 1.829 10⁻¹² F

when the plates separate at d = 9.60 10⁻³ m, the capcitance changes to

          C = ε₀ \frac{A}{d_1}

          C = 8.85 10⁻¹² 9.30 10⁻⁴/9.60 10⁻³

          C = 8.57 10⁻¹³ F

a) the potential difference

            C =

since the capacitor is not discharged, let's look for the initial charge

            Co = \frac{Q}{ \Delta V}

             Q = C₀ ΔV

              Q = 1.829 10⁻¹² 7.80

             Q = 14.2662 10⁻¹² C

when the condensate plates are separated

             C = \frac{Q}{ \Delta V' }

              ΔV ’= Q / C

              ΔV ’= 14.266 10⁻¹² / 8.57 10⁻¹³

              ΔV ’= 1.66 10¹ V= 16.6 V

b) the stored energy is

             U = ½ C ΔV²

for initial separation

              U = ½ C₀ ΔV²

             U = ½ 1.829 10⁻¹² 7.80²

              U = 55.64 10⁻¹² J

c) The energy for end separation;

               U_f = ½ C DV’2

                U_f = ½ 8.57 10⁻¹³ 16,6²2

                U_f = 1.18 10⁻¹⁰ J

d) The work

as there are no losses, the work is equal to the variation of the energy

                W = ΔU = U_f -U₀

                 W = 1.18 10⁻¹⁰ - 55.64 10-12

                 W = 6.236 10⁻¹¹ J

The percentage of mechanical energy lost (converted into thermal energy) during the collision will be equal to 95.2%.

Kinetic energy is the term used in physics to describe the force that a moving item has.

It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except for variations in speed, the body retains the kinetic energy it gains during acceleration.

As per the information in the question,

Ball's mass, m₁ = 50 g = 0.05 kg

Speed  = v₀

Brick's Mass, m₂ = 1 kg

Assume the speed of the brick after the collision is v.

Use the equation of the principle of conservation of linear momentum,

\(m_1v_o+m_2u_2= v(m_1+m_2)\)

0.5(v₀) + 0 = v(1 + 0.05)

v = (0.05v₀)/1.05

v = 0.048v₀.

Then the total kinetic energy will be:

K.E(initial) = 1/2 × 0.05v₀² + 1/2 × 0.05 × 0²

K.E(initial) = 0.025v₀²

Then,

K.E(final) = 1/2 × (1.05) × (0.048v₀)²

K.E(final) = 0.0012v₀²

So, the amount of mechanical energy lost in collision,

= (0.025v₀² - 0.0012v₀²)/0.025v₀² × 100

= 95.2%.

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This question seems incomplete, the complete question may be:

A 50 g ball of clay traveling at speed vo hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. a. Find an expression for the speed of the brick after the collision in terms of vo. b. What percentage of the mechanical energy is lost (i.e. converted to thermal energy) in this collision?

a) The number of excess electrons on the sphere is 1.97 x 10^10 electrons.

b) There are 0.0000857 excess electrons per lead atom.

a) The elementary charge of a single electron is -1.6 x 10^-19 C. To find the number of excess electrons on the sphere, we can divide the total charge by the charge of a single electron:

-3.15 x 10^-9 C / (-1.6 x 10^-19 C/electron) = 1.97 x 10^10 electrons

b) To find the number of excess electrons per lead atom, we need to first find the number of lead atoms in the sphere. We can use the molar mass of lead and the mass of the sphere to find the number of moles of lead:

7.90 g / 207 g/mol = 0.0382 mol

Next, we can use Avogadro's number to find the number of lead atoms:

0.0382 mol x (6.02 x 10^23 atoms/mol) = 2.30 x 10^22 atoms

Finally, we can divide the number of excess electrons by the number of lead atoms:

1.97 x 10^10 electrons / 2.30 x 10^22 atoms ≈ 0.0000857 excess electrons per lead atom.

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The boat's average acceleration is  0.8 m/s².

Acceleration is defined as the rate change of velocity with time.

acceleration a = (Δv) / (Δt)

A motorboat starting from rest travels in a straight line on a lake. If the boat reaches a speed of 8.0m/s in 10s.

The final velocity v = 8 m/s and it starts from rest, then its initial velocity v = 0 m/s.

Time taken for the change in speed t = 10 s.

The acceleration is given by

a = (8 - 0)/ 10

a = 0.8 m/s²

Thus, the boat's average acceleration is 0.8 m/s².

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Answer:

Explanation:

To convert Celsius to Fahrenheit, use the following formula;

= (°C * 9/5) + 32

= (453 * 9/5) + 32

= 847.4 °F

To convert Celsius to Kelvin, use the following;

= °C + 273.15

= 453 + 273.15

= 726.15K

Answer:

Explanation:

Using the equation of motion v² = u²+2aS

v is the final velocity = 120km/hr

120km/hr = 120 * 1000/1 * 3600 = 33.3m/s

u is the initial velocity = 0m/s

a is the acceleration

S is the distance covered = 240m

On substituting the given parameters

33.3² = 0²+2a(240)

33.3² = 480a

1110 = 480a

a = 1110/480

a = 2.3125m/s²

Hence the minimum constant acceleration that the aircraft require to be airborne after a takeoff run of 240 m is 2.3125m/s²

The capacitance of the capacitor is 1.7 * 10^-4 F. The capacitance will increase when the voltage is increased.

If we hold the capacitance constant, a higher voltage applied to the capacitor will result in a greater amount of electrical charge stored on the capacitor. Conversely, if we hold the voltage constant, a capacitor with a higher capacitance will be able to store more electrical charge. In other words, the capacitance and the voltage are directly proportional to the amount of electrical charge that can be stored on a capacitor.

We know that;

q = CV

C = q/V

C =  0.0024 C/12 V

C = 1.7 * 10^-4 F

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Answer:

F₁ = 4 F₀

Explanation:

The force applied on the string by the ball attached to it, while in circular motion will be equal to the centripetal force. Therefore, at time t₀, the force on ball F₀ is given as:

F₀ = mv₀²/r   --------------- equation (1)

where,

F₀ = Force on string at t₀

m = mass of ball

v₀ = speed of ball at t₀

r = radius of circular path

Now, at time t₁:

v₁ = 2v₀

F₁ = mv₁²/r

F₁ = m(2v₀)²/r

F₁ = 4 mv₀²/r

using equation (1):

F₁ = 4 F₀

Answer:

6s

Explanation:

Assume it is dropped from rest and the gravitational acceleration is 10

By the equation of motion under constant acceleration:

\(s=ut+\frac{1}{2} at^2\)

180 = (0)t+10(t^2)/2

t = 6 or -6 (rejected)

t = 6 s

Carl Rogers, along with Abraham Maslowsignificantly contributed to the humanistic psychology movement through his development of the person-centered approach and his emphasis on the individual's subjective experience and potential for personal growth.

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According to the give value of the mass of lemonade and change in the temperature, the specific heat capacity of the lemonade is 3.81 J/kg/k.

The formula for the specific heat capacity (C) = Q/ m × ΔT

Q is energy added and the value, which is 334J

m is the mass of the lemonade, which is 300g = 0.3 kg

Δ T is the change in temperature, which is 19°C =(273+19)= 292 K

So, C = 334/ 0.3 × 292

         = 3.81 J/kg/k

So the specific heat capacity of the lemonade is 3.81 J/kg/k.

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Answer:

average velocity = \(\bf 900 \space\ km/h\)

Explanation:

We can find the average velocity using the following equation:

\(\boxed{average \space\ velocity = \frac{total \space\ distance \space\ travelled}{ \space\ time \space\ taken}}\) .

In this case:

• total distance travelled = 450 km

• time taken = 30 min = 0.5 h

Substituting these values into the equation:

\(average \space\ velocity = \frac{450 \space\ km }{ 0.5 \space\ h}\)

                          ⇒ \(\bf 900 \space\ km/h\)

Answer:

Explanation:

The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. This means that a system always has the same amount of energy, unless it's added from the outside

Given,

The net-work done on the system is

The increase in its internal energy is

By the first law of thermodynamics.

Put the given values,

Thus, the amount of net heat is -44 J.

Answer:

Invasive plants also degrade the environment by changing the species composition and the ecology of invaded ecosystems

Explanation:

Answer:

they can harm the enviroment by changing the species composition and the ecology of invaded ecosystems !!

Answer:

The Current decreases

Explanation:

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