4. A vehicle
accelerates from
0 km/h to
100 km/h in 10 s.
What is its average
acceleration?

Answer:

[tex]28\; \rm m \cdot s^{-1}[/tex].

Explanation:

Apply the SUVAT equation [tex]\left(v^2 - u^2) = 2\, a \, x[/tex], where:

Assume that going downwards corresponds to a positive displacement. For this question:

Solve this equation for [tex]v[/tex]:

[tex]\displaystyle v = \sqrt{2\, a\, x + u^2} = \sqrt{2\times 9.8 \times 40} = 28\; \rm m \cdot s^{-1}[/tex].

In other words, the rock reached a velocity of [tex]28\; \rm m\cdot s^{-1}[/tex] (downwards) right before it hits the ground.

Let [tex]v[/tex] be the velocity (in [tex]\rm m \cdot s^{-1}[/tex]) of this rock right before it hits the ground. Under the assumptions of this question, it would take a time of [tex]t = (v / 9.8)[/tex] seconds for this rock to reach that velocity if it started from rest and accelerated at [tex]9.8\; \rm m \cdot s^{-2}[/tex].

Note that under these assumptions, the acceleration of this rock is constant. Therefore, the average velocity of this rock would be exactly one-half the sum of the initial and final velocity. In other words, if [tex]u[/tex] denotes the initial velocity of this rock, the average velocity of this rock during the fall would be:

[tex]\displaystyle \frac{u + v}{2}[/tex].

On the other hand, [tex]u = 0[/tex] because this stone is released from rest. Therefore, the average velocity of this rock during the fall would be exactly [tex](v / 2)[/tex].

The displacement of an object over a period of time is equal to the length of that period times the average velocity over that period. For this rock, the length of this fall would be [tex]t = (v / 9.8)[/tex], while the average velocity over that period would be [tex](v / 2)[/tex]. Therefore, the displacement (in meters) of the rock during the entire fall would be:

[tex]\displaystyle \left(\frac{v}{2}\right) \cdot \left(\frac{v}{9.8}\right) = \frac{v^2}{19.6}[/tex].

That displacement should be equal to the change in the height of the rock, [tex]40\; \rm m[/tex]:

[tex]\displaystyle \frac{v^2}{19.6} = 40[/tex].

Solve for [tex]v[/tex]:

[tex]v = 28\; \rm m \cdot s^{-1}[/tex].

Once again, the speed of the rock would be [tex]28\;\rm m \cdot s^{-1}[/tex] right before it hits the ground.

Answer:

Explanation:

Ocean contains salty water which causes the object to float rather than sinking, So yes it's easy to swim in ocean than water without salt.

Answer:

10.0575 m/s

Explanation:

40.23 divide by 4

Answer:

it is 10.0575 m/s

Explanation:

The average speed is calculated by total distance/total time taken. Here, the distance is 40.23 meters and time is 4 seconds.

So, average speed = 40.23/4 m/s

= 10.0575 m/s

Answer: Stress can adversely affect sleep quality and duration, while insufficient sleep can increase stress levels. Both stress and a lack of sleep can lead to lasting physical and mental health problems.

Explanation:

Many report that there stress increases when the length and quality of their sleep decreases. When you do not get enough sleep, 21 percent of adults report feeling more stressed.

Answer: 4.speed

Explanation:

In this case, we know that the cart remains at a constant 20km/h.

Now, one could say that "the velocity remains constant, because it always is 20km/h"

But remember that velocity is a vector, so this has a direction, and if the cart is going around a turn, then the direction of motion is changing, which tell us that there is acceleration.

But the module of the velocity, the speed, remains constant at 20km/h.

Then the correct option is 4, speed.

Explanation:

a. For constant acceleration:

v_avg = ½ (v + v₀)

v_avg = ½ (60 m/s + 15 m/s)

v_avg = 37.5 m/s

b. a = (v − v₀) / t

a = (60 m/s − 15 m/s) / 20 s

a = 2.25 m/s²

c. x = v_avg t

x = (37.5 m/s) (20 s)

x = 750 m

Answer:lol I don’t know good qeustion

Explanation:

Answer:

A) P = 3.3 × 10^(-11) Pa

B) Amplitude of electric field = 1.931 N/C

Amplitude of magnetic field = 6.44 × 10^(-9) T

C) μ_av = 1.65 × 10^(-11) J/m³

D) 50% each for the electric and magnetic field

Explanation:

A) First of all let's calculate intensity.

I = P_av/A

We are given;

P_av = 777 KW = 777,000 W

Distance = 5 km = 5000 m

Thus;

I = 777000/(2π × 5000²)

I = 0.00495 W/m²

Now, the average pressure would be given by the formula;

P = 2I/C

Where C is speed of light = 3 × 10^(8) m/s

P = (2 × 0.00495)/(3 × 10^(8))

P = 3.3 × 10^(-11) Pa

B) Formula for the amplitude of the electric field is gotten from;

E_max = √[2I/(εo•c)].

Where εo is the Permittivity of free space with a constant value of 8.85 × 10^(−12) c²/N.mm²

I and c remain as before.

Thus;

E_max = √[(2 × 0.00495)/(8.85 × 10^(−12) × 3 × 10^(8))]

E_max = √3.72881355932

E_max = 1.931 N/C

Formula for amplitude of magnetic field is gotten from;

B_max = E_max/c

B_max = 1.931/(3 × 10^(8))

B_max = 6.44 × 10^(-9) T

C) Formula for average density is;

μ_av = εo(E_rms)²

Now, E_rms = E_max/√2

Thus;

E_rms = 1.931/√2

μ_av = 8.85 × 10^(−12) × (1.931/√2)²

μ_av = 1.65 × 10^(-11) J/m³

D) The energy density for the electric and magnetic field is the same. So both of them will have 50% of the energy density.

Answe

a)  Q = 0.820 10⁻⁹ C ,   b)  Q = -3.52 10⁻⁹ C

Explanation:

The electric field is given by the formula

         E = k q / r²

where E is a vector quantity, so it must be added as a vector

          E_total = E₁ + E₂

let's look for the two electric fields

           E₁ = k q₁ / r₁²

           E₁ = 9 10⁹  5.4 10⁻⁹ / 1.25²

           E₁ = 31.10 N / C

           E2 = k Q / r₂²

           E2 = 9 10⁹ Q / 0.625²

           E2 = 23.04 10⁹ Q N / C           (1)

now we can solve the two cases presented

a) The total field is

            E_total = 50.0 N / C towards + x

since the test charge is positive the electric field E1 points to the right in the direction of the + x axis, so the equation is

            E_total = E1 + E₂

             E₂ = E_toal - E₁

             E₂ = 50.0 -31.10

             E2 = 18.9 N /C

With the value of the electric field we can calculate the charge (Q) using equation 1

             E₂ = 23.04 10⁹ Q

              Q = E₂ / 23.04 10⁹

              Q = 18.9 / 23.04 10⁹

              Q = 0.820 10⁻⁹ C

the charge on Q is positive

b) E_total = -50.0 N / C

              E_total = E₁ + E₂

              E₂ = E_total - E₁

              E2 = -50.0 - 31.10

               E2 = -81.10 N /C

we calculate the charge

             Q = E2 / 23.04 10⁹

             Q = -81.1 / 23.04 10⁹

              Q = -3.52 10⁻⁹ C

for this case the charge is negative

Answer:

10 minutes: 10 km

1 minute: 10 ÷ 10 = 1 km

the speed of the truck is 1km/min

Answer:

1 kilometer/minute

Explanation:

If we want to find the speed, we must divide the distance by the time.

[tex]s= \frac {s}{t}[/tex]

The truck travels a distance of 10 kilometers in 10 minutes.

[tex]d= 10 km\\t=10 min[/tex]

Substitute the values into the formula and divide.

[tex]s=\frac{d}{t}[/tex]

[tex]s=\frac{10 km}{10min}[/tex]

[tex]s= 1 km/min[/tex]

The speed of the truck is 1 kilometer per minute.

Answer:

(A) 1.43secs

(B) -2.50m/s^2

Explanation:

A commuter backs her car out of her garage with an acceleration of 1.40m/s^2

(A) When the speed is 2.00m/s then, the time can be calculated as follows

t= Vf-Vo/a

The values given are a= 1.40m/s^2 , Vf= 2.00m/s, Vo= 0

= 2.00-0/1.40

= 2.00/1.40

= 1.43secs

(B) The deceleration when the time is 0.800secs can be calculated as follows

a= Vf-Vo/t

= 0-2.00/0.800

= -2.00/0.800

= -2.50m/s^2

Answer:

Explanation:

The question states that the chairs are spaced 20 m apart through a length of 1 km, or say, 1000 m.

It also does say that each chair weighs 250 kg, and as such the load is

M = 50 * 250

M = 12500.

Taking into consideration, the initial and final heights, we have

h1 = 0, h2 = 200 m

The work needed to raise the chairs,

W = mgh, where h = h2 - h1

W = 12500 * 9.81 * (200 - 0)

W = 2.54*10^7 J

The work is done at a rate of 10 km/h, and at a distance of 1 km, time taken would be

t = 1/10 = 0.1 h or say, 360 s

The power needed thus, is

P = W/t

P = 2.54*10^7 / 360

P = 68125 W, or 68 kW

Initial velocity, u = 0 m/s

Final velocity, v = 10 km/h = 2.78 m/s

Startup time, t is 17 s

Acceleration during the startup then is

a = (v - u)/t

a = 2.78/17

a = 0.163 m/s²

The power needed for the acceleration is

P = ½m [(v² - u²)/t]

P = ½ * 12500 * [2.78²/17]

P = 6250 * 0.455

P = 2844 W

Answer:

16 m.

Explanation:

From the question given above, we obtained the following data:

Initial velocity (u) = 0 m/s

Final velocity (v) = 8 m/s

Initial time (t1) = 0 sec

Final time (t2) = 2 secs

Net Displacement (ΔD) =?

Velocity is defined as the rate of change of the displacement of an object with time. Mathematically, it is expressed as:

Change in velocity (Δv) = change in displacement (ΔD) / change in time (Δt)

Δv = ΔD / Δt

Next we shall determine the change in velocity and time. This is illustrated below below:

Initial velocity (u) = 0 m/s

Final velocity (v) = 8 m/s

Change in velocity (Δv) =?

Change in velocity (Δv) = v – u

Change in velocity (Δv) = 8 – 0

Change in velocity (Δv) = 8 m/s

Initial time (t1) = 0 sec

Final time (t2) = 2 secs

change in time (Δt) =?

change in time (Δt) = t2 – t1

change in time (Δt) = 2 – 0

change in time (Δt) = 2 secs.

Finally, we shall determine the net displacement of the object as follow:

Change in velocity (Δv) = 8 m/s

change in time (Δt) = 2 secs.

Net Displacement (ΔD) =?

Δv = ΔD / Δt

8 = ΔD/2

Cross multiply

ΔD = 8 × 2

ΔD = 16 m

Therefore, the net displacement of the object is 16 m.

Answer:

-1.17 m/s²

Explanation:

Given:

v₀ = 20 mph = 8.94 m/s

v = 0 m/s

t = 7.63 s

Find: a

v = at + v₀

0 m/s = a (7.63 s) + 8.94 m/s

a = -1.17 m/s²

The acceleration of the plane will be:

"-1.17 m/s²".

According to the question,

Velocity, v₀ = 20 mph or,

                   = 8.94 m/s

and,

                v = 0 m/s

Time, t = 7.63 s

We know the relation,

→ v = at + v₀

By substituting the values,

  0 = a × 7.63 + 8.94

7.63a = - 8.94

      a = -[tex]\frac{8.94}{7.63}[/tex]

         = - 1.17 m/s²  

Thus the response above is correct.

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Answer:

Stefan-Boltzmann Law describes the power radiated from a black body in terms of its temperature. Specifically, the total energy radiated per unit surface area of a black body across all wavelengths per unit time is proportional to the fourth power of the black body's thermodynamic temperature

Explanation:

So we now know that

energy per unit area is = zigma x T^4

From this

T = temperature in kelvin

zigma is stefan boltzman constant

So

E/A = 5.67 x 10^-8 x (2200)⁴

= 1.33x 10^6 W/m^2

Answer:

merry go round and Ferris wheel have a constant acceleration due to the change in direction at every point.

Answer:

A merry-go-round is accelerating. Acceleration is a change in speed, direction, or both. Even though the speed of the merry-go-round does not change, its direction constantly changes as it spins.

Explanation:

Answer:

a is moving at 60m and the other object

Answer:

[tex]$ \frac{4\pi R}{V}$[/tex]

Explanation:

Given :

Mass of ball 1 = m

Mass of ball 2 = 2m

Since, R>>>d, the collision is head on.

Therefore, we get

[tex]$ \frac{v_1 -v_2}{V}=\frac{1}{2}$[/tex]

[tex]$ \therefore \frac{\text{velocity of seperation}}{\text{velocity of approach}}= v_1-v_2 = \frac{V}{2}$[/tex]

Relative velocity is given by V/2. So, we get the time when the masses will again collide as

[tex]$ t = \frac{2\pi R}{\frac{V}{2}}=\frac{4\pi R}{V} $[/tex]

Answer:

Option (2)

Explanation:

From the figure attached,

Horizontal component, [tex]A_x=A\text{Sin}37[/tex]

[tex]A_x=12[\text{Sin}(37)][/tex]

     = 7.22 m

Vertical component, [tex]A_y=A[\text{Cos}(37)][/tex]

    = 9.58 m

Similarly, Horizontal component of vector C,

[tex]C_x[/tex]  = C[Cos(60)]

     = 6[Cos(60)]

     = [tex]\frac{6}{2}[/tex]

     = 3 m

[tex]C_y=6[\text{Sin}(60)][/tex]

    = 5.20 m

Resultant Horizontal component of the vectors A + C,

[tex]R_x=7.22-3=4.22[/tex] m

[tex]R_y=9.58-5.20[/tex] = 4.38 m

Now magnitude of the resultant will be,

From ΔOBC,

[tex]R=\sqrt{(R_x)^{2}+(R_y)^2}[/tex]

   = [tex]\sqrt{(4.22)^2+(4.38)^2}[/tex]

   = [tex]\sqrt{17.81+19.18}[/tex]

   = 6.1 m

Direction of the resultant will be towards vector A.

tan(∠COB) = [tex]\frac{\text{CB}}{\text{OB}}[/tex]

                  = [tex]\frac{R_y}{R_x}[/tex]

                  = [tex]\frac{4.38}{4.22}[/tex]

m∠COB = [tex]\text{tan}^{-1}(1.04)[/tex]

             = 46°

Therefore, magnitude of the resultant vector will be 6.1 m and direction will be 46°.

Option (2) will be the answer.

Answer:

t=240s

Explanation:

Distance=120m

Acceleration=-5m/s^2

v=0

Let u=x m/s

Using equation v^2-u^2=2as:-

0-x=2(-5)(120)

-x=-1200

x=1200m/s

Using now equation v=u+at:-

0=1200+-5t

5t=1200

t=240s

If a car stops at 120 meters. If it has an acceleration of –5 meters/second², then it would take  6.928 seconds to stop.

The rate of change of the velocity with respect to time is known as the acceleration of the object.

As given in the problem a car stops at 120 meters. If it has an acceleration of –5 meters/second², then we have to find out how long it would take seconds to stop.

By using the second equation of motion,

s = ut + 1/2at²

The distance traveled by car before stopping = 120 meters

acceleration =  –5 meters/second²

-120 = 0 + 0.5×( –5)t²

t² = 120/2.5

t² =48

t = 6.928 seconds

Thus, the time taken by the car before stopping would be 6.928 seconds.

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Answer:

Explanation:

The elevator is moving with uniform speed and bolt will fall with acceleration due to gravity g .

Displacement of elevator when bolt starts falling

= 5.05 x 5.75 = 29 m

Let after time t bolt reaches the elevator

in time t , displacement of bolt = 1/2 g t²

= .5 x 9.8 x t² = 4.9 t²

displacement of elevator = 5.05 t

position of elevator = 29 + 5.05 t

According to question ,

29 + 5.05 t = 4.9 t²

4.9 t² - 5.05 t - 29 = 0

t = 3 s approx .

b )

Distance covered by the bolt

= 1 /2 g t²

= .5 x 9.8 x 9

= 44.1 m

Bolt must have to fall from a height of 44.1 m

or in terms of floor it is

44.1 / 3 = 15 th floor .

Answer:

b the voltage gain will decrease

Explanation:

Q=CV

Answer:

2.59×10¯²² Kgm/s

Explanation:

Data obtained from the question include:

Velocity of electron = 0.95c

Momentum =?

Next, we shall determine the velocity of the electron. This can be obtained as follow:

Velocity of electron = 0.95c

Velocity of Light (c) = 3×10⁸ m/s

Velocity of electron = 0.95c

Velocity of electron = 0.95 × 3×10⁸

Velocity of electron = 2.85×10⁸ m/s

Finally, we shall determine the mometum of the electron.

Momentum is simply defined as the product of mass and velocity. Mathematically, it is expressed as:

Momentum = mass x Velocity

Thus, with the above formula, we calculate the momentum of the electron as follow:

Mass of electron = 9.1×10¯³¹ Kg

Velocity of electron = 2.85×10⁸ m/s

Momentum of electron =?

Momentum = mass x Velocity

Momentum = 9.1×10¯³¹ × 2.85×10⁸

Momentum = 2.59×10¯²² Kgm/s

Therefore, the momentum of the electron is 2.59×10¯²² Kgm/s

Answer:

[tex]-10 m/s[/tex]

Explanation:

When two cars collide then the momentum of two cars will remains conserved

By momentum conservation equation

               [tex]m1v1i+m2v2i=m1v1f + m2v2f[/tex]

               [tex](100)(8)+(100)(-10)=(100v)+(100)(8)\\ v=-10 m/s[/tex]

Answer:

(a) 70cm³

(b) 805 grams

Explanation:

(a) V = L×B×H

= 7cm×5cm×2cm

= 35cm×2cm

= 70cm³

(b) Mass = Volume × Density

= 70cm³ × 11.5g/cm³

= 805 grams

Complete question is;

A satellite dish has the shape of a parabola when viewed from the side. The dish is 60 inches wide and 45 inches deep. How far is the receiver from the bottom of the dish if the receiver is placed at the focus?

Answer:

the receiver should be put 40 inches from the bottom of the dish on the concave side of the dish

Explanation:

The base of the dish would simply be the vertex of parabola.

Since we want to find how far the receiver is from the bottom, the place where we'll place the receiver is simply the focus of the parabola.

Now, for example, if this is a parabola that opens upward and has it's vertex at the origin, then half of the diameter at a height of 45 inches gives the two points (60, 22.5) and (-60, 22.5)

Standard form equation of parabola with vertex at origin and pointing upwards is given by;

x² = 4ay

Plugging in the values of x and y gives;

60² = 4a(22.5)

3600/90 = a

a = 40 inches

Thus, the receiver should be put 40 inches from the vertex on the concave side of the dish

Answer:

46041J

Explanation:

Using Energy lost= mgh

Changing to standard its we have

= 195*1000/3600=54.2m/s

So = 85*54.2*10= 46041J

Answer:

45167.15 J/s

Explanation:

mass of the man = 85 kg

The man's speed = 195 km/h = 195 x 1000/3600 = 54.167 m/s

The man's weight = mg

where

m is the mass

g is acceleration due to gravity = 9.81 m/s^2

weight = 85 x 9.81 = 833.85 N

The rate at which energy is removed from the man = speed x weight

==> 54.167 x 833.85 = 45167.15 J/s

The term that defines the ability to cause motion or create change is called force. Details about force can be found below.

Force is the physical quantity that denotes ability to push, pull, twist or accelerate a body and which has a direction.

Force is measured in Newtons and can be calculated by multiplying the mass of the body by its acceleration.

Therefore, it can be said that the term that defines the ability to cause motion or create change is called force.

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