What was the initial speed of a car if its speed is 40 m/s after 5 seconds of accelerating at -4 m/s²?
A. 50 m/s
B. 60 m/s
C. 25 m/s
D. 20 m/s

(a) The trip covers a total distance of 6.0 + 4.0 + 2.0 = 12.0 km, so the jogger's average speed is (12.0 km)/(2.0 h) = 6.0 km/h.

(b) The jogger undergoes a total displacement given by the vector

(6.0 km) i + (4.0 km) j + (-2.0 km) i = (4.0 km) (i + j)

where i is the unit vector pointing due East and j is the unit vector pointing due North. This vector has magnitude

||(4.0 km) (i + j)|| = (4.0 km) √(1² + 1²) ≈ 5.7 km

so the jogger's average velocity is approximately (5.7 km)/(2.0 h) ≈ 2.8 km/h.

If a large star explodes in a supernova and leaves a core that's 10 times the mass of the Sun, the core of the star would collapse.

A star can be defined as a giant astronomical object that contains a luminous sphere of plasma, and it is bounded together by its own gravitational force.

Based on astronomical information, if a large star explodes in a supernova and leaves a core that's 10 times the mass of the Sun, the core of the star would collapse due to its own gravity which creates a violent explosion known as a supernova.

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The football must have the speed of 0.03 m/s to have the same momentum.

What is momentum conservation:

here,

mass of football, m1 = 150 kg

mass of bullet, m2 = 15 g = 0.015 kg

speed of bullet, v2 = 300 m/s

According to conservation of momentum:

substituting the values in equation,

150* v1 = ( 0.015 )* (300)

v1 =  0.03 m/s

Hence,

The football must have the speed of 0.03 m/s to have the same momentum.

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The magnitude of the second charge needed to propel the first charge is 6,250 C.

The magnitude of the second charge is calculated by applying Coulomb's law as follows;

F = kq₁q₂/r²

where;

Fr² =  kq₁q₂

q₂ = Fr²/kq₁

q₂ = (100 x 750,000²)/(9 x 10⁹ x 1)

q₂ = 6,250 C

Thus, the magnitude of the second charge needed to propel the first charge is 6,250 C.

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Answer:

F=Gm1m2 / r2

Explanation:

F = force

G = gravitational constant

m_1 = mass of object 1

m_2 = mass of object 2

r = distance between centres of the masses

answer is in the attachment

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Betelgeuse is a supergiant star that by mass is classified as a high-mass star.

What is a celestial body:

Celestial bodies are natural objects that are a part of the massive universe. Even though the universe has vast expanses of empty space, it is inhibited by them. The following are the 7 categories in which the celestial bodies are classified in:

Thus, as Betelgeuse is a supergiant star that will eventually result in a supernova it is classified as a high-mass star.

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The adhesion forces between mercury and glass are far weaker than the cohesive forces between mercury atoms causing the meniscus in the capillary tube to be lower than the meniscus in the beaker.

The force operating at a border between two phases is measured as surface tension.

Surface tension at liquid-air interfaces is caused by the higher attraction of liquid molecules to each other than air molecules.

Due to the relatively strong attraction of water. Hence molecules of water have high surface tension.

Because the water wets the glass and seeps up the tube's side when it is contained in a glass tube, the meniscus of the water has a concave form.

The cohesive forces between mercury atoms, on the other hand, are far stronger than the adhesion forces between mercury and glass.

The meniscus in the capillary tube is, therefore, higher than the meniscus in the beaker, but with mercury, the meniscus in the capillary tube is lower than the meniscus in the beaker.

Hence, the meniscus in the capillary tube is lower than the meniscus in the beaker

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Answer:

The acceleration of a point on the wheel is 11.43 m/s² acting radially inward.

Explanation:

The centripetal acceleration acts on a body when it is performing a circular motion.

Here, a point on the bicycle is performing circular motion as the rotation of the wheel produces a circular motion.

The centripetal acceleration of a point moving with a velocity  and at a distance of  from the axis of rotation is given as:

a = v2/r

Here, V = 8m/ s,r = 0.70 m

∴ a = 8/0.70 = 11.43m/ s2

Therefore, the acceleration of a point on the wheel is 11.43 m/s² acting radially inward.
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A special purpose nozzles that are often lowered through holes or other openings to the cellar of an occupancy are called cellar nozzles.

What is a nozzle:

A nozzle is a device in which steadily flowing fluid can be made to accelerate by a pressure drop along the duct in a cross-sectional area.

So when a fluid flows through a nozzle, its velocity increases continuously and pressure decreases continuously.

There are different types of tips like hollow cone, solid cone or flat fan.

The cellar nozzle (also called a Bresnan nozzle) is designed to be used under the surface the operator is standing on.

Hence,

The cellar nozzles are often lowered through holes or other opening to the cellar of an occupancy.

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Answer:

because the a and the b both have ones next to them so a is 1 and b is 1 so the sum is 2 and the minus changes because it is within the two lines

Explanation:

The wavelengths for frequencies 910 and 2555 MHz are 32.9 and 11.7 cm respectively.

What is frequency:

Frequency describes the number of waves that pass a fixed place in a given amount of time.

What is wavelength:

It is defined as the distance in meter required to complete one circle.

here, two microwave frequencies are given

f1 = 910 MHz = 910* 10^6 Hz

f2 = 2555 MHz = 2555* 10^6 Hz

According to formula of frequency:

where

v is speed of wave.

f is frequency of wave.

All electromagnetic wave moves with same speed v = 3×10⁸ m/s.

for f1:

substituting the values in equation,

λ1 = v / f1

λ1 =  3×10⁸ / 910* 10^6

λ1 = 0.329 m

λ1 = 32.9 cm

for f2:

λ2 = v / f2

λ2 =  3×10⁸ / 2555* 10^6

λ2 = 0.117 m

λ2 = 11.7 cm

Hence,

the wavelengths for frequencies 910 and 2555 MHz are 32.9 and 11.7 cm respectively.

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Work done by the friction force is 110.77 J

Calculation of friction force:

here box has mass, m=5.9 kg

It slides the distance of, d=9.3 m

coefficient of kinetic friction is 0.206

Now we can say that,

net force on the object is applied force and friction force

The net force according to Newton's second law:

F(net)=m*a

F(applied) - f(friction) = m*a

The work done by friction force will be

W= -k*mg*d

here g is gravitational acceleration.

substituting the values we get,

W=-(0.206)*(5.3)(9.8)*(9.3)

W= -110.77 J

negative sign denotes the opposite direction.

work done by the friction force is 110.77 J

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Answer:

Every object on the surface of the earth is pulled towards its surface because of a force known as the gravitational force. It is a force of attraction that exists between any two objects with mass.

The gravitational force of the earth pulls every object towards the surface of the earth. Because of this, an object free in the air is accelerated. The acceleration caused by the gravitational force is known as the acceleration due to gravity.

The magnitude of the acceleration is constant in a downward direction.

Acceleration is the rate of change in velocity.

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The electric energy stored per unit cubic meter is 7.5×10^(-8) joule/m³.

To find the answer, we need to know about the electric energy density.

In a vacuum where the permittivity is 8.85× 10^(-12), the electric energy density is 1/2 ×ε₀ ×E²

Energy density= (1/2)× 8.854×10^(-12)×130²

                          = 7.5×10^(-8) joule/m³

Thus, we can conclude that the energy density is 7.5×10^(-8) joule/m³.

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The spring is stretched about 3.5cm from its natural length as the block moves in this circle.

Acceleration is given by formula = [tex]\frac{v^{2} }{r}[/tex] where,..... (1)

v= velocity and r = total distance

In this case r = L+Δx where,

L is the length of unstretched spring

Δx = Change in Spring length

According to Hooke's law

F=kΔx …..(2) where,

F= force , k is constant and Δx= change in spring length

Also,

F=ma …..(3) where,

F= force , m= mass of body and a = acceleration

From equation (2) and (3)

ma = kΔx

Now, from equation (1)

mv²/L+Δx = kΔx

mv² = kΔx(L+Δx)…. (4)

Total energy(E) = 1/2mv² + 1/2kx²

From equation (4)

E = 1/2kΔx(L+Δx) + 1/2kΔx²

By solving this equation, this becomes

kΔx² + 1/2kΔxL - E = 0

Given,

k=200N/m  L=50cm=0.5m  E=2J

Δx = 0.035 m = 3.5cm

Hence, the spring is stretched about 3.5cm from its natural length as the block moves in this circle.

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Answer:

M au = Fs - M g       au = upwards acceleration; Fs = scale reading

Fs = M (au + g)    scalar quantities where g is positive downwards and au is positive upwards - Fs is the net force acting on the person

If the acceleration is zero Fs = M g  and the scale reads the persons weight

If the elevator is decelerating then au is negative and the scale reading     Fs = (g - au) M     and the scale reading is less than the weight of the person

The equation that represents the principle of the lever balance is:

The principle of moments states when a body is in equilibrium, the sum of the clockwise moment about a point equals the sum of anticlockwise moment about that point.

A see-saw represents a balanced system of moments.

The sum of clockwise moment = The sum of anticlockwise moments.

Assuming W1 and W2 are clockwise moments and W3 and W4 are anticlockwise moments.

The equation will b:  W₁ + W₂ = W3 + W4

In conclusion, a balanced see-saw illustrates the principle of the lever balance.

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0.32 km

How to reach the answer:

The formula below provides the tsunami's speed in response to the query.

s = 356√d

when the tsunami's speed is 200 km/h, the equation's "s" is changed to "200," and the equation of speed is then expressed as follows.

200 = 356√d

The equation can be changed to compute the depth of the water as,

√d = 200÷356

√d = 0.562

Now on squaring both sides:

(√d)² = (0.562)²

d = (0.562)² = 0.316 or 0.32

Therefore the approximate depth of water for a tsunami travelling at 200km/h is 0.32 km

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An average velocity can be defined as the total distance covered by a physical object divided by the total time taken.

Mathematically, you can find average velocity (Vaverage) from acceleration (a) and time (t) by using this formula:

Average velocity = acceleration × time

Vaverage = at     .......equation A.

Also, you can find distance (d) from average velocity (Vaverage) and time (t) by using this formula:

Distance = average velocity × time

d = vt        .......equation B.

Now, putting the two equations together and substituting the Vaverage term in equation B:

d = (at) × t

d = at²

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Complete Question:

A. How do you find average velocity (Vaverage) from acceleration (a) and time (t)?

B. How do you find distance (d) from average velocity (Vaverage) and time (t)?

C. Now put the two equations together. Substitute your result in equation A for the (Vaverage) term in equation B. Your final equation should only have d, a, and t terms.

Diagram A will result in the movement of the block to the left as a result of the forces.

This is referred to an influence which is capable of changing the motion of an object.

Diagram A has equal upward and downward force and left side which is 60N is higher than the right side which has 20N. The block will therefore move to the left.

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0.36 J of work is done in stretching the spring from 15 cm to 18 cm.

To find the correct answer, we need to know about the work done to strech a string.

Thus, we can conclude that the work done is 0.36 J.

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Voltage is defined as the force that causes electrons to flow. That is option A.

A Voltage is defined as an electromotive force and the potential difference in charge between two points in an electrical field.

It is equally known as the force that causes electrons of a current to flow.

Mathematically, it's = V = current × resistance.

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The period of the voltage that has a frequency of 60Hz is 0.0166s. Details about period can be found below.

Period in physics refers to the length of time during which the same characteristics of a periodic phenomenon recur.

The period is measured in seconds and is denoted by T. It can be calculated by dividing 1 by the frequency of an oscillation because it is inverse of the frequency.

T = 1/60 = 0.0166s

Therefore, the period of the voltage that has a frequency of 60Hz is 0.0166s.

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The ball will return to the thrower's hand with a speed of 10 m/s.

What is straight upward motion:

It is the motion when an object is projected upward, it moves in the opposite direction of the force of gravity.

The velocity is negative while the object moves up and positive while it moves downward due to upward motion.

Here,

A ball is thrown straight upward, u = 10 m/s

final velocity since ball momentarily stops at highest point, v= 0 m/s

According to Newton's 3rd equation of motion:

where,

g = acceleration due to gravity = -9.8 m/s²

h = height

substituting the values,

2(-9.8)h = (0)² - (10)²

h = 100 / 19.6

h = 5.10 m/s

Now, we consider downward motion:

2gh = v² - u²

where,

g  = 9.8 m/s²

h = height = 5.10  m

v = return velocity of ball

u = 0 m/s

substituting the values,

2(9.8)(5.10 m) = V² - (0)²

V = √(99.96)

V = 9.99 m/s

V ≈ 10 m/s

Hence,

the ball will return to the thrower's hand with a speed of 10 m/s.

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I want to examine the surface of a planet that is covered by a thick atmosphere (which includes oxygen and contains a very thick layer of water clouds that never clears). What wavelength of electromagnetic radiation would I be smartest to use: radar waves.

Radars send out electromagnetic waves much like wireless computer networks and cell phones. The signals are despatched out as short pulses which can be reflected by objects of their route, in part reflecting returned to the radar.

The radio waves travel outward from the antenna at the velocity of light (186,000 miles or three hundred,000 km in keeping with the second) and keep going until they hit something.

Then some of them bounce back in the direction of the antenna in a beam of contemplated radio waves also visiting at the speed of light. the speed of the waves is crucially vital.

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To reach 01.kg/L concentration of salt in the tank will take around 18.9 min.

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.

A concentrated solution is one that has a relatively large amount of dissolved solute. A dilute solution is one that has a relatively small amount of dissolved solute.

The concentration ,C(t) of salt at time t is given by the mass x(t) at time t divided by the volume t + 100 at time t.

That is C(t) = x(t)/ (t+100)

So that,

C(t) = 0.2 -  [tex]\frac{2 * 10^4}{(t + 100)^4}[/tex]

The concentration of salt is 0.1 kg/L ,

we solve C(t) =0.1 ,

Giving the equation,

0.10.2 - [tex]\frac{2 * 10^4}{(t + 100)^4}[/tex]

t = [tex]100\sqrt[4]{2} -100[/tex]

≈ 18.9  minutes

Therefore,

To reach 01.kg/L concentration of salt in the tank will take around 18.9 min.

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The velocity of the cart at the bottom of the ramp is 6.42m/s

Given that 40N cart slides  from rest down a rough 6.0 m long ramp and the degree given is 30 and the friction force given is 6.0N

We need to find the  velocity of the cart at the bottom of the ramp

One of two types of energy is known as potential energy and is the latent energy present in an item at rest.

According to the rule of conservation of energy, energy can only be transformed from one form of energy to another and cannot be generated or destroyed.

Potential energy of the crate at the top =40N×6sin30°m=120J

Energy lost due to friction =6N×6m=36J

Let the speed of the crate at the bottom be v.

Applying the law of conservation of energy,

120−36=0.5×(40/g)×v2

Therefore,

v=6.42m/s

Hence the velocity of cart at the bottom of the ramp is 6.42m/s

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The temperature increase that is necessary to increase the power radiated from an object by a factor of 8 is to increase the temperature by a factor of 1.68.

Radiation is the emission of energy in the form of waves or particles through space.

The magnitude of radiation emitted by an object is given as;

E = kσT⁴

where;

E₁/T₁⁴ = E₂/T₂⁴

T₂⁴ = T₁⁴E₂/E₁

T₂⁴ = T₁⁴(8E₁) / E₁

T₂⁴ = T₁⁴8

T₂ = (T₁⁴8)^(¹/₄)

T₂ = 1.68T₁

Thus, the temperature increase that is necessary to increase the power radiated from an object by a factor of 8 is to increase the temperature by a factor of 1.68.

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Answer:

B

Explanation:

Angular speed=velocity/radius

5/0.85=5.9