quations (3.4) and (3.5) are equivalent expressions for Lagrange's equations.
Exercise 3.1 Using the Nielsen form, determine the equation of motion
for a mass m connected to a spring of constant k.
Exercise 3.2 Using the Nielsen form, determine the equations of motion
for a planet in orbit around the Sun. (Answer: mr - mro² = - GMm and
mrö +2mr00.)
3.2 Hamilton's principle
echanical system composed of N particles can be described by n = 3N
inande

Answers

Answer 1

Answer:Using the Nielsen form, determine the equation of motion for a mass m connected to a spring of constant k. Exercise 3.2 Using the

Explanation:


Related Questions

NASA wants a satellite to revolve around Earth 3 times a day. What should be the radius of its orbit if we neglect the presence of the Moon? (G = 6.67 × 10-11 N ∙ m2/kg2, Mearth = 5.97 × 1024 kg)

Answers

Answer:

Approximately [tex]2.03 \times 10^{7}\; {\rm m}[/tex].

Explanation:

Assume that the radius of this orbit is [tex]r[/tex].

Let [tex]m[/tex] denote the mass of this satellite and let [tex]M[/tex] denote the mass of the Earth. At a distance of [tex]r[/tex] from the center of the earth, the magnitude of the gravitational attraction on this satellite would be [tex]G\, m\, M / (r^{2})[/tex].

The question implies that the gravitational pull from the earth is the only significant force on this satellite. Hence, the net force on this satellite would be also [tex]G\, m\, M / (r^{2})[/tex].

The acceleration of this satellite would thus be [tex]a = (\text{net force}) / (\text{mass}) = G\, M / (r^{2})[/tex].

Let [tex]\omega[/tex] denote the angular velocity of this satellite. Since this satellite in in a circular motion, the acceleration on this satellite would need to satisfy [tex]a = \omega^{2} \, r[/tex].

In other words:

[tex]\begin{aligned} \frac{G\, M}{r^{2}} = a = \omega^{2} \, r \end{aligned}[/tex].

[tex]\begin{aligned} r &= \left(\frac{G\, M}{\omega^{2}}\right)^{1/3}\end{aligned}[/tex].

The question asks for a rotation of [tex]3\times (2\, \pi) = 6\, \pi\; {\text{rad}}[/tex] within a day, which is [tex]24 \times 3600\; {\rm s}[/tex]. The angular velocity of this satellite should be:

[tex]\begin{aligned}\omega = \frac{6\, \pi}{24 \times 3600\; {\rm s}} \end{aligned}[/tex].

Substitute this value into the expression for [tex]r[/tex] and evaluate:

[tex]\begin{aligned} r &= \left(\frac{G\, M}{\omega^{2}}\right)^{1/3} \\ &= \left(\frac{(6.67 \times 10^{-11}\; {\rm N \cdot m^{2} \cdot kg^{-2}}) \times (5.97 \times 10^{24}\; {\rm kg})}{((6\, \pi) / (24 \times 3600\; {\rm s}))^{2}}\right)^{1/3} \\ &\approx 2.03 \times 10^{7}\; {\rm m}\end{aligned}[/tex].

(Note that [tex]1\; {\rm N} = 1\; {\rm kg \cdot m \cdot s^{-2}}[/tex].)

Consider a concave spherical mirr or that has focal length f = +19.5 cm.
a) What is the distance of an object from the mirror's vertex if the image is real and has the same height as the object? Follow the sign rules.

Answers

The distance of an object from the mirror's vertex if the image is real and has the same height as the object is 39 cm.

What is concave mirror?

A concave mirror has a reflective surface that is curved inward and away from the light source.

Concave mirrors reflect light inward to one focal point and it usually form real and virtual images.

Object distance of the concave mirror

Apply mirrors formula as shown below;

1/f = 1/v + 1/u

where;

f is the focal length of the mirrorv is the object distanceu is the image distance

when image height = object height, magnification = 1

u/v = 1

v = u

Substitute the given parameters and solve for the distance of the object from the mirror's vertex

1/f = 1/v + 1/v

1/f = 2/v

v = 2f

v = 2(19.5 cm)

v = 39 cm

Thus, the distance of an object from the mirror's vertex if the image is real and has the same height as the object is 39 cm.

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Let's begin with a simple calculation of the weight of air using density. Find the mass of air and its weight in a living room that has a 4.3m×5.4m floor and a ceiling 2.9 m high. What are the mass and weight of an equal volume of water?

a. What volume of water would have a mass equal to the mass of air in the room?

Answers

1. The mass of the air, given the data is 85.88 Kg

2. The weight of the air is 841.624 N

3. The mass of an equal volume of water is 67338 Kg

4. The weight of an equal volume of water is 659912.4 Kg

5. The volume of water that would have a mass equal to the mass of air in the room is 8.588×10⁻² m³

How to determine the volume of the air

We shall determine the volume of the air in the room by finding the volume of the room.

Volume of air = volume of room

Volume of air = 4.3 × 5.4 × 2.9

Volume of air = 67.338 m³

1. How to determine the mass of the airVolume of air = 67.338 m³Density of air = 1.2754 kg/m³Mass of air = ?

Density = mass / volume

Cross multiply

Mass = Density × volume

Mass of air = 1.2754 × 67.338

Mass of air = 85.88 Kg

2. How to determine the weight of the airMass of air (m) = 85.88 KgAcceleration due to gravity (g) = 9.8 m/s²Weight of air (W) = ?

W = mg

W = 85.88 × 9.8

Weight of air = 841.624 N

3. How to determine the mass of equal volume of waterVolume of air = 67.338 m³Volume of water = Volume of air = 67.338 m³Density of water = 1000 kg/m³Mass of water = ?

Density = mass / volume

Cross multiply

Mass = Density × volume

Mass of water = 1000 × 67.338

Mass of water = 67338 Kg

4. How to determine the weight of equal volume of waterMass of water = 67338 KgAcceleration due to gravity (g) = 9.8 m/s²Weight of water (W) = ?

W = mg

W = 67338 × 9.8

Weight of air = 659912.4 Kg

5. How to determine the volume of water with equal mass of air Mass of air = 85.88 KgMass of water = Mass of air = 85.88 KgDensity of water = 1000 kg/m³Volume of water = ?

Volume = mass / density

Volume of water = 85.88 / 1000

Volume of water = 8.588×10⁻²

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How can i find Air velocity??????????????

Answers

Answer: By dividing airflow by duct cross section.

Explanation:

In short, air velocity in the ducts is calculated by dividing airflow by duct cross-section. Airflow is expressed as a simple number. Example: Air conditioner has a max. airflow of 600 CFM.

(refer to photo attached) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in the figure below. (Enter the magnitude of the electric field only.) _____N/C

If a charge of −4.72 µC is placed at this point, what are the magnitude and direction of the force on it? Magnitude _______N

Direction?

- toward the left
- upward
-downward
- toward the right

Answers

The electric field strength at a point 1.00 cm to the left of the middle is  -2.0 x 10⁷ N/C.

The magnitude of the force is 94.4 N and direction of the force on it towards the right.

Electric field strength

The electric field strength at a point 1.00 cm to the left of the middle is calculated as follows;

E = kq/r²

Electric field due to first charge

E1 = (9 x 10⁹ x 6 x 10⁻⁶)/(0.02)²

E1 = 1.35 x 10⁸ N/C

Electric field due to second charge

E2 =  -(9 x 10⁹ x 1.5 x 10⁻⁶)/(0.01)²

E2 = - 1.35 x 10⁸ N/C

Electric field due to third charge

E3 = - (9 x 10⁹ x 2 x 10⁻⁶)/(0.03)²

E3 = -2.0 x 10⁷ N/C

Net electric field

E = E1 + E2 + E3

E = +1.35 x 10⁸ N/C - 1.35 x 10⁸ N/C - -2.0 x 10⁷ N/C

E = -2.0 x 10⁷ N/C

Force on the charge −4.72 µC

F = Eq

F = - 2.0 x 10⁷ x -4.72 x 10⁻⁶

F = 94.4 N

Thus, the direction of the force will be towards the right.

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An object with an initial velocity of
0.12rad accelerates at 0.11rad over a
distance of 0.25 radians. What is the
final angular velocity of the object?
rad
S

Answers

Answer:

100rad because it angular velocity

Consider the f(x) = cos(x-C) function shown in the figure in blue color, where 0 ≤ C ≤ 2π. What is the value of parameter C for the function in the figure?
As a reference the g(x) = cos(x) function is shown in red color, and green tick marks are drawn at integer multiples of π.

Answers

The value of parameter C for the function in the figure is 2.

What is amplitude of a wave?

The amplitude of a wave is the maximum displacement of the wave. It can also be described at the maximum upward displacement of a wave curve.

f(x) = Acos(x - C)

where;

A is amplitude of the waveC is phase difference of the wave

What is angular frequency of a wave?

Angular frequency is  the angular displacement of any element of the wave per unit time.

From the blue colored graph; at y = 1, x = -2 cm

1 = cos(2 - C)

(2 - C) = cos^(1)

(2 - C) = 0

C = 2

Thus, the value of parameter C for the function in the figure is 2.

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An ultracentrifuge is spinning at a speed of 80,000 rpm. The rotor that spins with
the sample can be roughly approximated as a uniform cylinder of 10 cm radius
and 8 kg mass, spinning about its symmetry axis). In order to stop the rotor in
under 30 s from when the motor is turned off, find the minimum braking torque
that must be applied.
O-19.2 Nm
-17.2 Nm
O -15.2 Nm
O-11.2 Nm
O None of the above

Answers

D. The minimum braking torque that must be applied is -11.2 Nm.

Moment of inertia of the uniform cylinder

The moment of inertia of the uniform cylinder is calculated as follows;

I = ¹/₂MR²

where;

M is mass of the cylinderR is radius of the cylinder

I = (0.5)(8)(0.1²)

I = 0.04 kgm²

Minimum braking torque

τ = -Iα

where;

α is angular acceleration

α = ω/t

α = (80,000 x 2π/rev x 1 min/60s) / (30 s)

α =  (80,000 x 2π)/(60 x 30)

α = 279.25 rad/s²

τ = - ( 0.04 kgm²) x (279.25)

τ =  -11.2 Nm

Thus, the minimum braking torque that must be applied is -11.2 Nm.

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You are writing a short report to a familiar audience and plan to use an informal
writing style. What can you do to make your writing informal?
Use contractions such as won't, it's, let's, and we're.
Include second-person pronouns such as you.
Use passive-voice verbs.
Incorporate longer sentences.

Answers

The thing that the presenter can do to make the presentation to appear informal is to use contractions such as won't, it's, let's, and we're.

What is a report?

The term report refers to any formal presentation. It is usually made as part of an academic course or as part of professional development. It could be given while a person is hoping for promotion at a job that he or she is doing.

We have to bear in mind that the audience to whom the report is being presented is a familiar audience hence the presentation can be quite informal and devoid of the formality of presentation of reports as we know it to be.

Now, the focus is to make the presentation to look informal. The thing that the presenter can do to make the presentation to appear informal is to use contractions such as won't, it's, let's, and we're.

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Complete the following:

When light is incident parallel to the principal axis and then strikes a lens, ___

the light will remain parallel after refracting through the lens
the light will refract through the focal point on the opposite side of the lens
the light will not refract at all

Answers

When light is incident parallel to the principal axis and then strikes a lens, the light will refract through the focal point on the opposite side of the lens.

To find the answer, we have to know about the rules followed by drawing ray-diagram.

What are the rules obeyed by light rays?If the incident ray is parallel to the principal axis, the refracted ray will pass through the opposite side's focus.The refracted ray becomes parallel to the major axis if the incident ray passes through the focus.The refracted ray follows the same path if the incident light passes through the center of the curve.

Thus, we can conclude that, when light is incident parallel to the principal axis and then strikes a lens, the light will refract through the focal point on the opposite side of the lens.

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"The acceleration due to gravity on the surface of the earth is 9.8 m/s ²." What does it mean?​

Answers

Answer:  It simply means that a freely falling object would increase its velocity by 9.8 m/s per second

Answer:

Hello!

"The acceleration due to gravity on the surface of the earth is 9.8 m/s ²." What does it means that

That every second an object is in free fall, gravity will cause the velocity of the object to increase 9.8 m/s. So, after one second, the object is traveling at 9.8 m/s.

Why is glass classified the way it is?
A. The bulb lights up when the switch is closed.
B. Free electrons can carry charge.
C. Delocalized electrons create a current.
D. Not enough charge carriers.

Answers

The glass is classified the way it is because of option(b)i.e, Free electrons can carry a charge.

An amorphous solid is a glass. Glass shows all the mechanical properties of a solid even though its atomic-scale structure resembles that of a supercooled liquid. Transparency, heat resistance, pressure and breakage resistance, and chemical resistance are among glass' primary properties. 90% of all manufactured glass is soda-lime glass, making it the most prevalent and least priced type.

High electronegativity and tightly bonded electrons are found in the oxygen atoms that make up glass. This is so that glass can conduct electricity, which requires a significant amount of energy to release the electrons from the oxygen atom. As a result, the glass serves as an insulator at room temperature.

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Why does the ball orbit the Earth when launched from the theoretical cannon of Newton?
A. it gets stuck in the atmosphere
B. it is magnetically attracted
C. it is attached by a rope to the Earth
D. it falls at the same rate the Earth curves

Answers

The ball orbit the Earth, when launched from the theoretical cannon of Newton, is option B. it is magnetically attracted.

Newton's Cannonball:

Newton's cannonball was a hypothetical situation. Isaac Newton once proposed that gravity, which he believed to be a universal force, was the primary factor behind the planetary motion. In this experiment, Newton imagines projecting a stone or a cannonball onto the summit of a very tall mountain. The body should move away from Earth in the direction it was projected if there were no effects from gravity or air resistance.

Depending on the projectile's initial velocity and the gravitational force acting on it, the bullet will travel in a different direction. Low speeds result in a simple fallback to Earth. The Earth's surface causes the cannonball to deviate from its elliptical route.

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In thicker materials the particles can move more easily, therefore the resistance has to ____________.
A. Increase
B. Decrease
C. Stay the same
D. Not enough info

Answers

In thicker materials the particles can move more easily, therefore the resistance has to decrease.

Hence Option (b) is correct.

Resistivity, which is sometimes represented by the Greek letter rho, is quantitatively equal to a specimen's resistance R times its cross-sectional area A times its length.

ρ = R × A/ l

R = ρ × l/ A

It means the Resistance of the material is inversely proportional to the area of the material.

As the area of the material increases, the resistance decreases and vice versa.

Hence, In thicker particles, there is a greater area available and that's why resistance has to decrease so that particles can move more easily.

Hence, Option (b) is correct.

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*example of previous incorrect/correct answer on similar question) Inside a vacuum tube, an electron is in the presence of a uniform electric field with a magnitude of 330 N/C.

(a) What is the magnitude of the acceleration of the electron (in m/s²)?
__________m/s²

(b) The electron is initially at rest. What is its speed (in m/s) after 8.00 ✕ 10−⁹ s?
______m/s

Answers

The final speed of the electron is 4.64 * 10^5 m/s.

What is the speed of the electron?

Given that the mass of the electron is obtained as 9.11 * 10^-31 Kg, we have that the charge of the electron is 1.6 * 10^-19 C.

E= F/q

F = Eq

F =  330 N/C * 1.6 * 10^-19 C

F = 5.28 * 10^-17 N

F = ma

a = F/m = 5.28 * 10^-17 N/ 9.11 * 10^-31 Kg

a = 5.8 * 10^13 m/s^2

Using

v = u + at

u = 0 m/s because the electron was initially at rest

v = at

v = 5.8 * 10^13 * 8.00 ✕ 10−⁹ s

v = 4.64 * 10^5 m/s

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The Sun subtends an angle of about 0.5∘ to us on Earth, 150 million km away.
Estimate the radius of the Sun.
Express your answer to two significant figures and include the appropriate units.

Answers

The radius of the Sun is approximately 654497.9 kilometers.

A subtended angle in geometry is an angle created by a common point (in this case, the Earth) that crosses two points of a nearby circular arc (the Sun in this case). Below is a visual illustration of the subtended angle.

The law of cosine can be used to calculate the sun's radius, which is 654497.950 kilometers in kilometers.

The Sun's radius is nearly 109 times bigger than the Earth's. The Earth's radius is 6378 kilometers. Or to put it another way, both dimensions are 1: 109 ratios.

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explain the use of low energy x-ray?​

Answers

Answer:

The low energy X-ray calibration service is intended for thin-window plane-parallel chambers required for the dosimetry of superficial X-ray beams. Low-energy X-ray therapy is also known as superficial radiation therapy. This therapy uses beams of low-energy X-rays (radiation waves) to destroy skin cancer cells while not harming healthy tissue around or under the upper layers of skin.

which element has more than 5 valency​

Answers

Answer:

Sulfur (Has six valence electrons). It has maximum valency due to belonging to VI groups of the Periodic Table.

Explanation:

The electrons found in an element's outermost atomic shell are known as valence electrons.

Sulfur, which has an atomic number of 16, has an electrical configuration of 2, 8, 6, meaning it has six electrons in its outermost shell. As a result, its valence electrons will also be six.

However, in its natural condition, sulfur exists as the S8 molecule, which has the classic chair structure where each sulfur atom is covalently connected to two other sulfur atoms. In that sense, there will be 8 valence electrons.

Consequently, the answer will be 6 if you're asking about the "sulphur atom," but 8 if you're talking about sulfur in general.

Thank you ,

Eddie

If something is a good conductor, what type of insulator is it?

1. also a good insulator
2. a metal
3. it depends
4. a poor insulator

Answers

4. a poor insulator

If rest other things are kept constant or unchanged then a good conductor can be termed as a poor insulator.

Answer:

4 conductors and insulators are opposites of each other.

Explanation:

Friction typically __________ objects. A. Speeds up B. Slows down C. Doesn't affect D. Destroys

Answers

Answer:

B

Explanation:

friction opposes motion

Friction typically Slows down objects

Option "B"

How does friction affect speed?Friction and Speed

While this is almost true for a wide range of low speeds, as speed increases and air friction is reckoned with, it has been found that friction depends not only on speed, but also on speed squared and sometimes on higher powers of friction. speed.

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*please refer to photo* An electric field of magnitude 5.25 ✕ 10^5N/C points due south at a certain location. Find the magnitude and direction of the force on a
−7.35 C charge at this location.

Magnitude _____N

Direction?
- north
-south
-east
-west

Answers

Answer:

Approximately [tex]3.86\; {\rm N}[/tex] (given that the magnitude of this charge is [tex]-7.35\; {\rm \mu C}[/tex].)

Explanation:

If a charge of magnitude [tex]q[/tex] is placed in an electric field of magnitude [tex]E[/tex], the magnitude of the electrostatic force on that charge would be [tex]F = E\, q[/tex].

The magnitude of this charge is [tex]q = 7.35\; {\rm \mu C}[/tex]. Apply the unit conversion [tex]1\; {\rm \mu C} = 10^{-6}\; {\rm C}[/tex]:

[tex]\begin{aligned} q &= 7.35\; {\mu C} \times \frac{10^{-6}\; {\rm C}}{1\; {\mu C}} = 7.35\times 10^{-6}\; {\rm C}\end{aligned}[/tex].

An electric field of magnitude [tex]E = 5.25\times 10^{5}\; {\rm N \cdot C^{-1}}[/tex] would exert on this charge a force with a magnitude of:

[tex]\begin{aligned}F &= E\, q \\ &= 5.25 \times 10^{5}\; {\rm N \cdot C^{-1}} \times (-7.35\times 10^{-6}\; {\rm C}) \\ &\approx 3.86\; {\rm N}\end{aligned}[/tex].

Note that the electric charge in this question is negative. Hence, electrostatic force on this charge would be opposite in direction to the the electric field. Since the electric field points due south, the electrostatic force on this charge would point due north.

A block and tackle pulley system has 3pulley wheels in the lower movable block. Determine the load that can be lifted by an effort of 350N if the efficiency of the system is 80%​

Answers

A block and tackle pulley design has a velocity ratio 3. <br> Draw a labelled diagram of this system. In your diagram, indicate absolutely the points of application and the directions of the load and effort

How to calculate  the load that can be lifted by an effort of 350N if the efficiency of the system is 80%​?

VR =3

VR = n=3

Efficiency of the system = 80%

Thus , Mechanical asvantage [tex]$=V R \times \eta=$[/tex]80/100×3 =2.4

Man can lift load with effort =350N

Thus,

Load= MA× effort = 2.4×350 = 840 N.

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How does the suns energy affect the climate of an area

Answers

Answer:

the earth receives the suns energy as radiation which is able to travel without the need of matter from point A to point B and this radiation is also in the form of heat.

Explanation:

Sun's energy fall on the earth in form of radiation and heats up the atmosphere and produces unequal heating due to its spherical nature and impacts climate of different areas.

The Sun is the only source of energy for the Earth's climate system. Fundamental to atmospheric composition is the warming of the atmosphere caused by solar radiation, which also causes global wind patterns and aids in the development of clouds, storms, and rainfall.

When the sun is at its maximum (peak in sunspots, prominences, and flares), it produces more ultraviolet (UV) radiation. More ozone is produced as a result of UV light, warming the stratosphere. The lower atmosphere and Earth's surface warm slightly as a result of the increased solar radiation.

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Consider the f(x) = cos(Bx) function shown in the figure in blue color. What is the value of parameter B for this function? This parameter is called angular frequency in physics and it is denoted by ω.
As a reference the g(x) = cos(x) function is shown in red color, and green tick marks are drawn at integer multiples of π.

Answers

The value of parameter B (angular frequency) for this function is 2.7.

What is amplitude of a wave?

The amplitude of a wave is the maximum displacement of the wave. It can also be described at the maximum upward displacement of a wave curve.

f(x) = Acos(Bx)

where;

A is amplitude of the waveB is angular frequency of the wave

What is angular frequency of a wave?

Angular frequency is  the angular displacement of any element of the wave per unit time.

From the blue color; at y = -0.9, x = -7.5 cm

-0.9 = cos(-7.5B)

7.5B = arc cos (0.9)

7.5B = 2.7

B = 7.5/2.7

B = 2.7

Thus, the value of parameter B (angular frequency) for this function is 2.7.

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If the gravitational potential energy of an object 10 m above the ground is 50 J, what is its Ep, if it moves to 30 m above the ground?​

Answers

Answer:

150 J

Explanation:

Moving 3 times higher will increase the   P E  x 3   = 150 J

a 30kg crate is pulled up a ramp 15m long and 2m high by a constant force of 100n. the crate starts from resta nd has a velocity of 2m/s when it reaches the ramp. what is the frictional force between the crate and the ramp. use the principal of conservation energy.​

Answers

The frictional force between the crate and the ramp is determined as 35.2 N.

Energy lost to frictional force

Apply the principle of conservation energy to calculate the change in the energy of the crate.

Change in energy of the crate = energy loss to friction

P.Ei - K.Ef = E

mgh - ¹/₂mv² = E

where;

m is mass of the crateh is vertical height traveled by the cratev is the final velocity of the crate

(30)(9.8)(2) - (0.5)(30)(2²) = E

528 J = E

Frictional force between the crate and the ramp

E = Fd

where;

F is the frictional forced is the distance traveled by the crate

F = E/d

F = (528)/(15)

F = 35.2 N

Thus, the frictional force between the crate and the ramp is determined as 35.2 N.

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Complete the missing information from the circuit

Answers

From the first circuit (see attached), it is correct to state that I₄ = 40mA. See the explanation below.

What is a circuit?

A path that is designed to transport electric current is that is referred to as a circuit.

How do we compute for the missing details?

I = 200mA

= 20mA + 140mA + I₄

I₄ = 200 - 160

I₄ = 40mA

From the above, we can rightly posit:

R₄ = 3/(40x 10⁻³)

= 75 Ω

Hence

V₆ =  V₄ - V₅

= 3v - 2v

= 1v

R₆ therefore, =

V₆/I₆

= 1/ (40 x 10 ⁻³)

= 14.28 Ω

I₃ = I₄ + I₆

= 40 + 140

= 180mA

R₃ = 9/(180 x 10⁻³)

= 50Ω

R₂ = 12/20 x (10⁻³)

= 60 Ω

Then,

Vbattery =

200 x 10⁻³ x90

= 18 volts

The above indices is used to complete the image. See Circuit Image II.

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A tree limb is blown loose from a tree during a storm. As it falls, it gains
speed. Which type of energy is the tree limb gaining as it falls?
O A. Kinetic energy
B. Gravitational potential energy
O C. Nuclear energy
OD. Light energy

Answers

Answer:

B Gravitational potential energy

Explanation:

how to calculate the half time​

Answers

The formular for calculating half life is:

T1/2=0.693/Π

accelerates uniformly at 2.0 ms2 for 10.0s. Calculate its final velocity​

Answers

Answer:

The distance is

=

7

m

Explanation:

Apply the equation of motion

s

(

t

)

=

u

t

+

1

2

a

t

2

The initial velocity is

u

=

0

m

s

1

The acceleration is

a

=

2

m

s

2

Therefore, when

t

=

3

s

, we get

s

(

3

)

=

0

+

1

2

2

3

2

=

9

m

and when

t

=

4

s

s

(

4

)

=

0

+

1

2

2

4

2

=

16

m

Therefore,

The distance travelled in the fourth second is

d

=

s

(

4

)

s

(

3

)

=

16

9

=

7

m

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