A truck travels on a straight road at a velocity of 17 meters per second. Over 20

seconds, it accelerates uniformly to 27 meters per second. What distance did the truck

travel during this acceleration?

Answer:

a)   v = 26.2 m / s, b) acceleration is radial, a = 27.4 m / s², c)   a = 2.8 g and

d) a = - 8.73 10⁻² m / s²,  τ = 1.09 10⁴ N m

Explanation:

a) For this exercise we can use the relationships between rotational and linear motion

           v = w r

let's reduce the magnitudes to the SI system

          w = 10 rpm (2pi rad / 1 rev) 1 min / 60s) = 1,047 rad / s

          r = 25.0 m

let's calculate

          v = 1.047 25.0

          v = 26.2 m / s

b) When the body is rotating at constant speed, the relationship must be perpendicular to the speed, therefore the direction of acceleration is radial, that is, towards the center of the circle and its magnitude is

            a = v² / r

            a = 26.2²/25

            a = 27.4 m / s²

c) Let's look for the relationship between the centripetal acceleration and the acceleration due to gravity

           a / g = 27.4 / 9.8

           a / g = 2.8

           a = 2.8 g

d) let's find the deceleration and torque to stop the centripette in 5 min

           t = 5 min (60 s / 1min) = 300 s

let's use the rotational kinematics relations

           w = w₀ + α t

initial angular velocity is wo = 1,047 rad / s and the final as is stop do w = 0

           α = - w₀ / t

           α = - 1,047 / 300

           α = -3.49 10⁻³ rad / s²

angular and linear are related

           a = α r

           a = -3.49 10⁻³ 25

           a = - 8.73 10⁻² m / s²

the negative sign indicates that the acceleration is stopping the movement

torque is

           τ = F r

The force can be found with Newton's second law

          F = m a

we substitute

         τ = m a r

         τ = 5000.0   8.73 10⁻²  25

         τ = 1.09 10⁴ N m

Answer:

a. i. -4.65 m/s ii. -13.95 m/s b. 5.89 m c. 2.85 s

Explanation:

a. What is the velocity of the box at (i) t = 1.00 s and (ii) t = 3.00 s?

We write the equation of the forces acting on the mass.

So, T - mg = ma where T = tension in vertical rope = (36.0 N/s)t, m = mass of box = 3.50 kg, g = acceleration due to gravity = 9.8 m/s² and a = acceleration of box = dv/dt where v = velocity of box and t = time.

So, T - mg = ma

T/m - g = a

dv/dt = T/m - g

dv/dt = (36.0 N/s)t/3.50 kg - 9.8 m/s²

dv/dt = (10.3 m/s²)t - 9.8 m/s²

dv = [(10.3 m/s²)t - 9.8 m/s²]dt

Integrating, we have

∫dv = ∫[(10.3 m/s³)t - 9.8 m/s²]dt

∫dv = ∫(10.3 m/s³)tdt - ∫(9.8 m/s²)dt

v = (10.3 m/s³)t²/2 - (9.8 m/s²)t + C

v = (5.15 m/s³)t² - (9.8 m/s²)t + C

when t = 0, v = 0 (since at t = 0, box is at rest)

So,

0 = (5.15 m/s³)(0)² - (9.8 m/s²)(0) + C

0 = 0 + 0 + C

C = 0

So, v = (5.15 m/s³)t² - (9.8 m/s²)t

i. What is the velocity of the box at t = 1.00 s,

v =  (5.15 m/s³)(1.00 s)² - (9.8 m/s²)(1.00 s)

v = 5.15 m/s - 9.8 m/s

v = -4.65 m/s

ii. What is the velocity of the box at t = 3.00 s,

v =  (5.15 m/s³)(3.00 s)² - (9.8 m/s²)(3.00 s)

v = 15.45 m/s - 29.4 m/s

v = -13.95 m/s

b. What is the maximum distance that the box descends below its initial position?

Since v = (5.15 m/s³)t² - (9.8 m/s²)t and dy/dt = v where y = vertical distance moved by mass and t = time, we need to find y.

dy/dt = (5.15 m/s³)t² - (9.8 m/s²)t

dy = [(5.15 m/s³)t² - (9.8 m/s²)t]dt

Integrating, we have

∫dy = ∫[(5.15 m/s³)t² - (9.8 m/s²)t]dt

∫dy = ∫(5.15 m/s³)t²dt - ∫(9.8 m/s²)tdt

∫dy = ∫(5.15 m/s³)t³/3dt - ∫(9.8 m/s²)t²/2dt

y = (1.72 m/s³)t³ - (4.9 m/s²)t² + C'

when t = 0, y = 0.

So,

0 = (1.72 m/s³)(0)³ - (4.9 m/s²)(0)² + C'

0 = 0 + 0 + C'

C' = 0

y = (1.72 m/s³)t³ - (4.9 m/s²)t²

The maximum distance is obtained at the time when v = dy/dt = 0.

So,

dy/dt = (5.15 m/s³)t² - (9.8 m/s²)t = 0

(5.15 m/s³)t² - (9.8 m/s²)t = 0

t[(5.15 m/s³)t - (9.8 m/s²)] = 0

t = 0 or [(5.15 m/s³)t - (9.8 m/s²)] = 0

t = 0 or (5.15 m/s³)t = (9.8 m/s²)

t = 0 or t = (9.8 m/s²)/(5.15 m/s³)

t = 0 or t = 1.9 s

Substituting t = 1.9 s into y, we have

y = (1.72 m/s³)t³ - (4.9 m/s²)t²

y = (1.72 m/s³)(1.9 s)³ - (4.9 m/s²)(1.9 s)²

y = (1.72 m/s³)(6.859 s³) - (4.9 m/s²)(3.61 s²)

y = 11.798 m - 17.689 m

y = -5.891 m

y ≅ - 5.89 m

So, the maximum distance that the box descends below its initial position is 5.89 m

c. At what value of t does the box return to its initial position?

The box returns to its original position when y = 0. So

y = (1.72 m/s³)t³ - (4.9 m/s²)t²

0 = (1.72 m/s³)t³ - (4.9 m/s²)t²

(1.72 m/s³)t³ - (4.9 m/s²)t² = 0

t²[(1.72 m/s³)t - (4.9 m/s²)] = 0

t² = 0 or (1.72 m/s³)t - (4.9 m/s²) = 0

t = √0 or (1.72 m/s³)t = (4.9 m/s²)

t = 0 or t = (4.9 m/s²)/(1.72 m/s³)

t = 0 or t = 2.85 s

So, the box returns to its original position when t = 2.85 s

Answer:

making sense of a 3-d world from 2-d data

Explanation:

Answer:

The balls velocity is 1 divided by 3

The velocity of the ball is 18.85 m/s.

The ball’s centripetal acceleration is 236.87 m/s².

The ball's centripetal force is  118.44 Newton.

Centripetal acceleration is a characteristic of an object's motion along a circular path. Centripetal acceleration applies to any item travelling in a circle with an acceleration vector pointing in the direction of the circle's center.

Given parameters:

length of the string: l = 1.5 meters.

Time interval = 60 seconds.

Total number of complete rotation = 120.

Hence, the velocity of the ball = 120×2π×1.5/60 m/s

= 18.85 m/s.

The ball’s centripetal acceleration = (velocity)²/ radius

= (18.85)²/1.5 m/s²

= 236.87 m/s²

The ball's centripetal force = mass × centripetal acceleration

= 0.5 × 236.87 Newton

= 118.44 Newton

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Answer:

84kliometers

Explanation:

divide one hundred and sixty eight kilo meters by two hours

Answer:

a) time taken to catch up with speeding car is 12.25 secs

b) the police car will travel 273.8 m to catch up with the speeding car

Explanation:

Given that;

speed of car [tex]V_{c}[/tex] = 50 mi/hr = 22.352 m/s

acceleration of police car = 10 mi/hr = 4.47 m/s²

[tex]V_{f}[/tex]  = 70 mi/hr = 31.29 m/s

Now time taken to reach maximum speed is t₁

so

[tex]V_{f}[/tex] =  [tex]V_{i}[/tex] + at₁

we substitute

31.29 = 0 + 4.47t₁

t₁ = 31.29 / 4.47

t₁  = 7 sec

now

d₁ = 0 + 1/2 × at₁²

d₁ = 0 + 1/2 × 0 + 4.47×(7)²

d₁ = 109.5 m

so distance travelled by the speeding car in time t₁  will be

[tex]d_{c}[/tex] = [tex]V_{c}[/tex] × t₁

we substitute

[tex]d_{c}[/tex] = 22.352 × 7

[tex]d_{c}[/tex]  = 156.46 m

now distance between polive car and speeding car

Δd =  [tex]d_{c}[/tex] - d₁

Δd = 156.46 - 109.5

Δd = 46.96 m

time taken to cover Δd will be

t₂ = Δd / ( [tex]V_{f}[/tex] - [tex]V_{c}[/tex] )

t₂ = 46.96 / ( 31.29 - 22.352 )

t₂ = 46.96 / 8.938

t₂ = 5.25 sec

distance travelled by the police in time t₂ will be

d₂ = [tex]V_{f}[/tex] × t₂

d₂ = 31.29 × 5.25

d₂ = 164.3 m

a) How long will it take before the officer catches up to the speeding car;

time taken to catch up with speeding car;

t = t₁ + t₂

t = 7 + 5.25

t = 12.25 secs

Therefore, time taken to catch up with speeding car is 12.25 secs

b)  how far will it have travelled in order to do so;

distance = d₁ + d₂

distance = 109.5 + 164.3

distance = 273.8 m

Therefore, the police car will travel 273.8 m to catch up with the speeding car

Answer:

The time of motion is 0.64 s.

Explanation:

Given;

mass of the apple, m = 107 g

height of fall, h = 2 m

The velocity of the apple when it hits the ground is calculated from the law of conservation of energy;

[tex]P.E = K.E\\\\mgh = \frac{1}{2} mv^2\\\\gh = \frac{1}{2} v^2\\\\v^2 = 2gh\\\\v = \sqrt{2gh} \\\\v = \sqrt{2\times 9.8\times 2} \\\\v = 6.261 \ m / s[/tex]

The time of motion is calculated;

v = u + gt

6.261 = 0 + 9.8t

6.261 = 9.8t

t = 6.261 / 9.8

t = 0.64 s

Therefore, the time of motion is 0.64 s

The time taken for the apple to hit the ground is 0.64 s.

The time taken for the apple to hit the ground can be calculated using the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Solve for t.

Hence, The time taken for the apple to hit the ground is 0.64 s

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Answer:

Speed of the melon = 0.25 m/s

we would normally don't see the melon moving due to friction with the resting surface.

Explanation:

We use conservation of momentum:

Pi = Pf

with Pi = 0.1 kg * 30 m/s = 3 kg m/s

and Pf = 0.1 kg * 20 m/s + 4.0 kg * V = 2 kg m/s + 4 * V

Then using the equality above, we solve for V (velocity of the melon)

3 kg m/s = 2 kg m/s + 4 V

1 kg m/s = 4 kg * V

Then V = 1 / 4  M/s = 0.25 m/s

So we would normally don't see the melon moving due to friction with the resting surface.

Answer:

C: Equal to

Explanation:

In calculating workdone, it is pertinent to know that it doesn't depend on time. The only relationship between work and time is when we want to calcite power where workdone/time taken = power.

Now, even if it took 2T time to love the same distance, it just means lesser force was used but still the workdone doesn't change.

Thus, the workdone in the first case will be equal to the workdone in the second case.

Answer:

Untrasound

Explanation:

Your welcome :)

Answer:

Q = 1.2*10⁻¹² C

Explanation:

       [tex]C = \frac{Q}{V} (1)[/tex]

       [tex]C = \frac{\epsilon_{0}*\epsilon _{r} * A}{d} (2)[/tex]

       [tex]Q =\frac{\epsilon_{0} * \epsilon_{r} *A* V}{d} = \frac{(8.85*(4.7)^{2}*79.5)e-24 (F/m*m2*V)}{1.3e-8m} = 1.2e-12 C = 1.2 pC (3)[/tex]

Answer:

the required speed/velocity of the stunt double is 13.633 km/h

Explanation:

Given the data in the question;

velocity of train V = 150 km/h

distance = length of train + distance between the tunnel and the end

= 2 km + 20 km = 22 km

first we calculate time t taken by the train to reach the tunnel;

t = distance / velocity

we substitute

t = 22 km / 250 km/h

t = 0.1467 hr

so the velocity of the of the stunt double will be;

velocity = distance / time

we substitute

velocity = 2 km / 0.1467 hr

velocity = 13.633 km/h

Therefore, the required speed/velocity of the stunt double is 13.633 km/h

Answer:

Water > Box of books > Stone > Ball

Explanation:

We'll begin by calculating the potential energy of each object. This can be obtained as follow:

For stone:

Mass (m) = 15 Kg

Acceleration due to gravity (g) = 10 m/s²

Height (h) = 3 m

Potential energy (PE) =?

PE = mgh

PE = 15 × 10 × 3

PE = 450 J

For water:

Mass (m) = 10 Kg

Acceleration due to gravity (g) = 10 m/s²

Height (h) = 9 m

Potential energy (PE) =?

PE = mgh

PE = 10 × 10 × 9

PE = 900 J

For ball:

Mass (m) = 1 Kg

Acceleration due to gravity (g) = 10 m/s²

Height (h) = 20 m

Potential energy (PE) =?

PE = mgh

PE = 1 × 10 × 20

PE = 200 J

For box of books:

Mass (m) = 25 Kg

Acceleration due to gravity (g) = 10 m/s²

Height (h) = 2 m

Potential energy (PE) =?

PE = mgh

PE = 25 × 10 × 2

PE = 500 J

Summary:

Object >>>>>>>> Potential energy

Stone >>>>>>>>> 450 J

Water >>>>>>>>> 900 J

Ball >>>>>>>>>>> 200 J

Box of books >>> 500 J

Arranging from greatest to least, we have:

Object >>>>>>>> Potential energy

Water >>>>>>>>> 900 J

Box of books >>> 500 J

Stone >>>>>>>>> 450 J

Ball >>>>>>>>>>> 200 J

Water > Box of books > Stone > Ball

Explanation:

The energy of the system before the collision must equal the energy after the collision.

After the collision the bullet and the block have a total mass of 18.41 kg and they move at a speed of 8.8 m/s. The kinetic energy after the collision is

[tex]\frac{18.41 kg (8.8 m/s)^2}{2} = 713 J[/tex]

Before the collision only the bullet has kinetic energy.

So we can now determine the speed of the bullet using

[tex]\frac{0.11kg (v^2)}{2} = 713 J\\v = 114 m/s[/tex]

Answer:

8.5 hours

Explanation:

Answer:

I.72m/s²

II.8m/s²

Explanation:

acceleration equal velocity² divided by length

Answer:

b 1.39 m/s²

Explanation:

Given the following data;

Time = 12 seconds

Distance, S = 100 m

Since it's starting from rest, the initial velocity is equal to 0m/s.

To find the acceleration, we would use the second equation of motion;

[tex] S = ut + \frac {1}{2}at^{2}[/tex]

Where;

S represents the displacement or height measured in meters.

u represents the initial velocity measured in meters per seconds.

t represents the time measured in seconds.

a represents acceleration measured in meters per seconds square.

Substituting into the equation, we have;

100 = 0(12) + ½*a*12²

100 = 0 + 72

100 = 72a

Acceleration, a = 100/72

Acceleration, a = 1.389 ≈ 1.39 m/s²

Answer:

in the acceleration process the quantity α and w must increase

the deceleration process the alpha quantity must constant  a direction opposite to the angular velocity

Explanation:

Acceleration and angular velocity are related to linear

           v = w xr

            a = αx r

The bold letters indicate vectors and the cross is a vector product, therefore if

we can see that the relationship between linear and angular variables is direct

therefore in the acceleration process the quantity α and w must increase as well as their linear counterparts

in the deceleration process the alpha quantity must constant as the linear acceleration and must have a direction opposite to the angular velocity

Answer:

Explanation:

The distance of searchlight will act as radius R and velocity of car may be supposed to be tangential velocity v  . We are required to calculate  angular velocity ω .

v = 80 ft /s

R = 3000 ft

ω = v / R

= 80  / 3000 = .027 rad / s

For angular acceleration the formula is

angular acceleration α = a / R

a is linear acceleration = 15 ft / s²

α = 15 / 3000 = .005 rad / s².

Answer:

A. 2.63 s B. 12.38 m

Explanation:

A. For what time interval (in s) after the light turned green is the bicycle ahead of your car?

The time interval at which the bicycle is ahead of the car is the time it takes for the car to reach the bicycle's speed of 21.0 mi/h.

So, using v = u + at where u = initial speed of car = 0 mi/h, v = final speed of car = 21.0 mi/h, a = acceleration of car = 8.00 mi/h/s and t = time taken for acceleration.

So, v = u + at

t = (v - u)/a

substituting the values of the variables into the equation, we have

t = (21.0 mi/h - 0 mi/h)/8.00 mi/h/s

= 21.0 mi/h ÷ 8.00 mi/h/s

= 2.63 s

B. By what maximum distance does the bicycle lead the car?

To find this distance, we find the distance moved by both the car in this time of t = 2.63 s

So, using s = ut + 1/2at² where u = initial speed of car = 0 mi/h = 0 m/s, t = time = 2.63 s, a = acceleration of car = 8.00 mi/h/s = 8.00 × 1609 m/3600 s = 3.58 m/s/s = 3.58 m/s² and s = distance moved by car.

So, substituting the values of the variables into the equation, we have

s = ut + 1/2at²

s = 0 m/s × 2.63 s + 1/2 × 3.58 m/s² × (2.63 s)²

s = 0 m + 1/2 × 3.58 m/s² × (2.63 s)²

s =  1.79 m/s² × 6.9169 s²

s = 12.38 m

which is also the maximum distance with which the bicycle leads the car.

Answer: 1. The law of consevation of energy sates that energy can neither be created nor destroyed. It can only be transformed or transfered from one form to another. The law of conservation of energy is found everywhere for example, Water falls from the sky, converting potential energy to kinetic energy.

2. Different forms of energy are related because energy cannot be created or destroyed. they can all be transformed into from one form to another.

Explanation:

Answer:

10s

Explanation:

Horizontal velocity is the velocity of an object in an horizontal direction

The ball's horizontal velocity is approximately 33.078 ft./s

Reason:

The known parameter are;

The horizontal distance the footballer kicks the ball, d = 43 yards

The time after which the ball lands, Δt = 3.9 seconds

Required:

To find the velocity of the ball

Solution:

[tex]Velocity = \dfrac{Distance}{Time} = \dfrac{d}{\Delta t}[/tex]

Therefore;

[tex]Horizontal \ velocity \ of \ the \ ball, \ v_x= \dfrac{43 \ yard}{3.9 \ seconds} \approx 11.026 \ yd/s[/tex]

The ball's horizontal velocity, vₓ ≈ 11.026 yd/s

1 yard = 3 feet

[tex]11.026 \ yard = 11.026 \ yard \times \dfrac{3 \ feet}{yard} = 22.078 \ feet[/tex]

The ball's horizontal velocity, vₓ ≈ 33.078 ft./s

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Answer:

B. in both directions until the temperature is equal in the water and the air

Explanation:

When a warm body is in contact with a cool body , there is exchange of heat energy in both sides until there is attainment of equilibrium temperature . At this temperature both the body attains equal temperature . Initially rate of heat radiated by warm body is more than that from cool body , but after attainment of equilibrium , the rate becomes equal to each other . This is called dynamic equilibrium .

Hence option B is correct .

when the photosynthetic began to pump free oxygen into oceans, the ocean had enough oxygen to support the life of non-photosynthetic organisms. So, non-photosynthetic organisms came into being.

Answer:

its x and y component is 24.749m/s

Explanation:

Given

Speed of the dog = 35m/s

x component of the speed = xcos theta

y component of the speed = ycos theta

Given theta =45 degrees

x-component = 35cos45

x-component = 35(0.7071)

x-component = 24.749m/s

y-component = 35sin45

y-component = 35(0.7071)

y-component = 24.749m/s

Hence its x and y component is 24.749m/s

Answer:

7 would be C, a cell.

Explanation:

Hi.

7 would be C, a cell.

A cell is the basic unit of structure and function in all living things.

If it is living, it is made of cells.

Hope this helps.

Answer:

7. Cell

8. Organelle

Answer:

a)  v = 4.37 10⁶ m / s,  speed is much less than c

b)     v = 2.01 10⁸  m / s,  this value is 67% of the speed of light, , for which relativistic corrections should be used

Explanation:

The bohr model for the hydrogen atom and dendroids is a classical model with a quantization of the angular momentum

let's start by using Newton's second law with the electric force

         F = m a

Coulomb's law electric force

         F = [tex]k \frac{q_1q_2}{r^2}[/tex]

in this case in an atom the number of protons is equal to the atomic number and there is only one electron

        q₁ = Ze

        q₂ = e

acceleration is centripetal

         a = v² / r

we substitute

        [tex]k \frac{Z e^2}{r^2} = m \frac{v^2}{r}[/tex]

        v² =  [tex]k \frac{Ze^2}{m r}[/tex]

quantization is imposed without justification in this model,

       L = p x r = n [tex]\hbar[/tex]

       \hbar= h /2π

if we consider circular orbits, the speed and position are perpendicular

       m v r = n \hbar

       r = [tex]\frac{n \hbar}{m v}[/tex]

we substitute

     v² = [tex]k \frac{Z e^2}{m} \frac{m v}{n \hbar}[/tex]

     v = [tex]k \frac{Z e^2 }{ n \hbar}[/tex]

let's apply this equation

     \hbar= h / 2π

     \hbar= 6.626 10-34 / 2π

     \hbar= 1.05456 10⁻³⁴ J s

a) He1 ion,  the atomic number of helium is 2

      v =  [tex]\frac{9 \ 10^9 \ 2 ( 1.6 \ 10^{-19})^2 }{n \ 1.0546 \ 10^{-34}}[/tex]

       v =4.3695 10⁶ / n m / s

the ground state occurs for N = 1

        v = 4.37 10⁶ m / s

the relationship of this value to the speed of light is

        v / c = 4.37 10⁶/3 10⁸

        v / c = 1.46 10⁻²

speed is much less than c

b) the uranium ion with atomic number Z = 92

       v = [tex]\frac{9 \ 10^9 \ 92 ( 1.6 \ 10^{-19})^2 }{n \ 1.054 \ 10^{-34} }[/tex]

       v = 2.01 10⁸  m / s

       v/c = [tex]\frac{2.01 \ 10^8 }{3 \ 10^8}[/tex]

       v/c =  0.67

this value is 67% of the speed of light, for atoms with a higher atomic number the effects are increasingly important, for which relativistic corrections should be used