CBSE Class 9 Science Wave Motion And Sound Notes

WAVE MOTION AND SOUND

NATURE OF SOUND

Sound is a form of energy which effects our sensation of hearing through the ear. The sensation is produced by longitudinal waves in an elastic medium, where the vibrations (oscillations) of the particles are in the same direction in which the wave propagates.

PRODUCTION OF SOUND WAVES

In laboratory sound is produced by a tuning fork by striking its one prong on a soft rubber pad. Sound can also be produced by plucking a stretched string (violin), by blowing flute, by striking tabla and many other ways.

PROPAGATION OF SOUND

Take a tuning for (a source of standard frequency). It is set into vibrations and its prongs A and B are kept vertical. The prongs move in and out from their means position and have a transverse vibratory motion. When the prongs are in means position, the air in their surrounding has normal density. (It is shown in figure (a) with equidistant lines). As the right prong moves out onwards right, it pushes the air layers to the right. This produces a compression (It is shown in figure (b) with closer  lines).The prong returns inwardly to mean position. The compression moves to the right. The air near the prong again has normal density as shown in figure (c). As the prong continues moving toward s extreme left, vacating the space, density of air falls in the region and a rarefaction is produced (It is shown in figure (d) with spread lines). As the prong moves back to right extreme, it competes one vibration. Also the motion of the prong produces a new compression. This completes one wave.Since on vibration of the prong has generated one wave in the medium (air), in one second and many waves will be generated as the number of vibrations that the tuning fork will make in one second. This number is called frequency of the tuning fork (This number is engraved on the tuning fork near the bend). Hence we conclude that the wave frequency (the number of waves being generated per second) is equal to the frequency of the tuning fork.

SOUND NEEDS A MATERIAL MEDIUM FOR ITS PROPAGATION

An electric ell is enclosed inside an inverted bell jar by hanging from the rubber cork. The jar is closed at the bottom by an airtight place with a hole in the  centre. A pipe through the hole leads out to a vacuum pump (pump which draw the air out a vessel).

The bell is connected to a battery through a key.

The bell is started by closing the key. Initially when jar has normal air inside it, sound waves produced by the ringing bell heard outside the jar.

The vacuum pump is started and the air form inside the jar is gradually drawn out. With decreases air inside the jar, sound heard becomes weaker and weaker. After sometime no sound is heard, though the bell hammer is seen in vibration.

Conclusion :

In the absence of medium (air) around the source, sound is not being propagated.

A natural fact : Moon has no atmosphere. The space above the atmosphere is also vacuum. If some explosion takes place on moon, sound of the explosion will not be propagated to the earth. So the sound waves never reach the earth.

CHARACERISTICS OF SOUND WAVE

(i) Pitch :

Pitch is the sensation (brain interpretation) of the frequency of an emitted sound.

Faster the vibration of the source, higher is the frequency and higher is the pitch. Similarly low pitch sound corresponds to low frequency.

A high pitch sound is called a shrill sound (Eg : humming of a bee, sound of guitar etc.)

A low pitch sound is called a hoarse sound (Eg : roar of a lion, car horn etc.)

(ii) Loudness or softness :

Loudness or softness of sound wave is the sensations that depends upon is amplitude. When we strike a table to with more force, it vibrates and produces loud sound waves which have more amplitude. When struck with smaller force, vibrating table top produces soft sound waves which have less amplitude. A loud sound wave carries more energy and can be heard at large distance. Reduction in amplitude at large distance, makes the sound soft.

(iii) Timbre or quality :

Quality or timbre is characteristic of a sound which enables us to distinguish between the sound of same loudness and pitch. This characteristic of sound helps up to recognise our friend from his voice without seeing him. The quality of two sounds of same loudness and pitch produced by two different sources are distinguishable because of different wave form produced by them.

 Eg. : The violin and flute (Bansuri)

(iv) Intensity :

Intensity of a sound is defined at the sound energy transferred per unit area placed perpendicular to the direction of the propagation of sound.

That is, intensity of sound = sound energy/  Time x Area

Intensity of a sound is an objective physical quantity. It does not depend on the response of our ears.

The S.I. unit of intensity of sound is joule s^-1 m^-2 watt m^-2                    ( Js^-1 = 1W)

              Difference between loudness and intensity of sound :

RANGE OF HEARING

The human ear is able to h ear sound in a frequency range of about 20Hz to 20kHz. We can not hear sounds of frequencies less than 20Hz of more than 20kHz, these limits vary from persons to person and with age. Children can her sounds of somewhat higher frequencies, say upto 30 kHz. With age, our ability to hear high frequency sound diminishes. For the elder, the upper limit often falls to 10^-12 kHz. We take 20Hz-20 kHz as the audible range for a average person.

Even in the audible range the human ear is not equally sensitive for all frequency. it is mot sensitive to frequencies around 2000-3000 Hz.

Sound of frequencies less than 20 Hz is known as infrasonic sound or infrasound. Sound of frequency greater than 20 kHz is known as ultrasonic or ultrasound.

Different animals have different ranges of audible frequencies. A dog can hear sound of frequencies upto about 50 kHz and a bat upto about 100 kHz. Dolphins can hear sounds of even higher frequencies. Animals such as elephants and whales can hear sounds of frequencies less than 20 Hz. Some fishes can hear sounds of frequencies as low as 1-25 Hz.

SONIC BOOM

When a body moves with a speed which is greater than the speed of sound in air, it is said to be traveling at supersonic speed. Jet fighters, bullets, etc, often travel at supersonic speed. And when they so son, they produce a sharp, loud sound called a sonic boom.

The source moves at a speed greater then that of sound waves traveling at the speed of sound, are left behind. The high-pressure layers due to sound waves originating at different points bunch together as shown in figure. Actually, these layers fall on the surface of an imaginary cone of which OA, OB is a part. The total pressure on the surface of this cone is very high. The source is at the apex of this cone. As the source moves ahead, It drags the cone together with it. When the surface of the cone reaches a person, the ears experience a sudden increase in pressure. After the surface crosses him, the pressure is suddenly reduced. This causes the person to hear a sharp, loud sound-the sonic boom.

A region consisting of a very-high-pressure layer followed by a lower-pressure layer travels through the space together with the cone. This is called a shock wave. This shock wave give rise to the sonic boom when it reaches a person. The shock waves produced by supersonic aircraft have enough energy to shatter glass and even damage weak buildings.

REFLECTION OF SOUND

When sound waves strike a surface, hey return back into the same medium. This phenomenon is called reflection. The reflection of sound waves is similar to that of light rays. The only difference is that sound waves being larger in length. require bigger surfaces for reflection

(a) Laws of Reflection :

(i) Angle of incidence is equal to the angle of reflection.

(ii) The incident wave, the reflected wave and the normal, all lie in the same plane.

(b) Verification of Law of Reflection :

Take a smooth polished large wooden board and mount it vertically on the table. At right angle to the board, fix a wooden screen. One each side of the screen, place a long, narrow and highly polished tube 9inside). Place a clock at the end of he tube A. Move the tube B slightly from left to right, till a distinct tick of clock is heard. Measure the < PCN  and   

(c) Applications of Reflection of Sound :

(i)  Mega phone or speaking tube :

When we have to call someone at a far off distance (say 100m), we cup our hands and call the persons with maximum sound we can produce. The hands percent the sound energy from spreading in all directions. In the same way, the people use horn shaped metal tubes, commonly called megaphones. The loud speakers have horn shaped openings. In all these devises, the sound energy is prevented from spreading out by successive reflections from the horn shaped tubes.

(ii) Stethoscope :

It is an instrument used by the doctors for listening sound produced within the body, empirically in the heart and lungs. In the stethoscope, the sound produced within the body of a patient to picked up by a sensitive diaphragm and then reaches the doctors ears by multiple reflection.

(iii) Sound board :

The sound waves obey the laws of reflection on the place as well as curbed reflecting surfaces. In order to spread sound evenly in big halls or auditoriums, the speaker (S) is fixed at the principle focus of the concave reflector. This concave reflector is commonly called sounding board. The sound waves striking the sound board get reflected parallel to the principal axis.

SPEED OF SOUND IN DIFFERENT MEDIUM

Sound travels with different speed in different media like solid, liquid and gas. This is because, sound travels in a medium due to the transfer of energy from one particle to another particle of the medium.

Solid : Since the particles of solid are close to each other, so transfer of energy from one particle to another takes place in less time (i.e. faster). Hence speed of sound in solids is large.

Liquid : Speed of sound in liquids in less than in solids since the particles are away from each other as compared to solids.

Gas :Speed of sound in gases is  less than the speed in liquids and solids as the particles are far always as compare to slides and liquids.

EFFECT OF TEMPERATURE ON THE SPEED OF SOUND

Sound travels faster as the temperature of the medium increases and vice-versa. This happens because as temperate increases, the particles of the medium collide more frequently and hence the disturbance spreads faster.

Speed of sound in air increases by 0.61  m/s with every 1⁰C increases in temperature. For example if speed of sound in air at 0⁰C is 330 m/s, then its speed at 25⁰C will be 345 m/s.

 Speed of sound does not depend on the pressure of the medium if temperature of the medium remains.

ECHO

The sound heard after reflection from a rigid obstacle is called on echo.

It is of three types :

(a) Instantaneous echo    (b) Syllabic echo (c) Successive echo

(a) Instantaneous Echo :

The echo of sound of short duration (like clap, pistol shot) is called instantaneous echo. It is found that sensation of any sound persists for 1/10  to 1/20 seconds in our ear, after it, the existing sound dies off. This time is called persistence of sound or persistence of hearing. It varies from persons to person and also with frequency of sound. We will use 1/15 second as a typical interval needed to distinguish two sounds.

(b) Syllabic Echo :

The echo of syllables of spoken words is called syllabic echo.

This echo is clear when the sound of last syllable of speech is reflected from an obstacle at least 22 m away so that sound takes atleast (2/15) second during which the last syllable is compactly spoken.

(c) Successive Echo :

This echo is head when sound is produced between two distant parallel rows of tall buildings or hills. A number of echoes are heard successively due to the multiple reflection. This echo is heard only in vast open field.

RELATION BETWEEN SPEED OF SOUND, TIME OF HERING ECHOAND DISTANCE OF

 REFLECTING BODY                                                                                                                              

If t is the time at which an echo is heard, d is the distance between the source of sound and the reflecting body and v is the speed of sound. The total distance traveled by the sound is 2d.

Speed of sound,   v= 2d/ t

or                   d= vt / 2         

(a) Calculation of Minimum Distance of Hearing Echo :

d is minimum distance required for hearing an echo when persistence of hearing is 1/15 second. The velocity of sound (at room temperature) is 340 m/s.

So,        d= vt / 2  =340/2  x 1/15 = 2267/2      

11 metre is the minimum distance of hearing echo.

(b) Conditions for Formation of an Echo :

(i) The minimum distance between the source of sound and the reflecting body should be 11 metres.

(ii) The wavelength of the sound should be less than the height of the reflecting body.

 (iii) The intensity of sound should e sufficient so that it can be heard after reflection.

 REVERBERATION

Persistence of sound after its production is stopped. is called reverberation.

When a sound is produced in a big hall, its wave reflect from the walls and travel back and forth. Due to this, energy does not reduce and the sound persists.

Small amount of reverberation for lesser time helps in adding volume to the programmers. Too much reverberation confuses the programmers and must be reduced.

To reduce reverberation, the rood and walls of the hall are covered with a sound absorbing materials like rough plaster and thick curtains.

AUDIBLE, INFRASONIC AND ULTRSONIC WAVES

(a) Audible Range :

The human ear is sensitive to sound waves of frequency between 20Hz to 20 kHz. This range is known as audible range.

Eg.: By vibrating sitar, guitar, organ pipes, flutes, shehnai etc.

(b) Infrasonic Wave :

A longitudinal elastic wave whose frequency is below the audible range i.e. 20 Hz, is called an infrasonic wave  it is generally generated by a large source.

 Eg. : Earthquake.

 (c) Ultrasonic Wave :

A longitudinal wave whose frequency is above the upper limit of audible range i.e. 20 kHz, is called ultrasonic wave. it is generated by very small sources.

Eg. : Quarts crystal.

ULTRASOUND

 Sound of very high frequency (greater than 20 kHz) is called ultrasound.

Production :  These are produced by electric oscillator using high frequency vibrations of quarts crystal.

Properties : Sound wave of all frequencies carry energy with them, with increase in frequency, vibration becomes faster and also energy consents and force increase. When ultrasound travels in solid, liquid and gas it subjects the particles of matter to face large force and energy.

(a) Applications of ultrasound :

(i) Welding metal :

They are used for welding metals like tungsten which cannot be welded by conventional methods. One of the two pieces of the tungsten is held firmly against the other piece and then vibrated with an ultrasonic vibrator. The heat produced due to friction, sat the point of contact, melts the melts. On stopping the vibrator, the melted ends of metals fuse to form a tight weld.

(ii) Medial purposes :

The ultrasonic vibrations can be reflected from the boundaries between the materials of nearly same density. The technique is used in scanning the internal organs of human body. It is superior to the X-ray scanning, as it does not cause any harm to human cells, unlike X-rays.

The instrument which used ultrasonic waves for getting the images of internal organs of human body is called ultrasound scanner. In this technique, the ultrasound waves travel through the tissues of the body and get reflected from the region where there is change in density. These reflected waves are then converted into electrical signals. These signals are then displayed on T.V. monitor or can e printed on  a film.

This technique is called ultrasonography and help doctors to deted abnormalities, such as stone in gall bladder and kidney or tumours in different organs.

Ultrasound waves of high intensity are employed to break small stones in the kidney into find grains. The find grains then get flushed out with urine.

(iii) Drilling holes or making cuts of desired shape :

We can use a hammer and a steel punch to make holes in metal plates, plastic sheets or other solid materials. Such holes an also be made using ultrasonic vibrations produced in a metallic rod, called a horn. The horn acts like a hammer, hammering the plate about hundred thousand times per second. The shape of the hole is the same as the of the tip of the hom. The shape of the tip can be designed as per the requirement of the application. ultrasonic cutting and drilling are very effective for fragile material like glass, for which ordinary methods do not give good results.

(iv) Ultrasonic cleaning :

We normally clean dirty clothes, places or other large objects by applying detergent or organic solutions, rubbing and washing. But for small parts such as those used in watches, electronic components, odd-shaped parts such as a spiral tube and parts located in hard-to reach places, this method is inconvenient and sometimes impossible. Such objects are placed in a cleaning solution and ultrasonic waves are sent into the solution. Because of vibrations at high frequencies, all dirt and grease particles get detached from the surface and object gets thoroughly cleaned.

(v) ultrasonic detection of defects in metals :

Metallic components are used in buildings, bridges, machines, scientific equipments and so on. If there are cracks or holes inside the metal used, the strength of the structure or component is reduced and it can fail. Such defects are not visible from the outside. ultrasonic waves can be used to detect such defects.

Ultrasonic waves are sent through the metallic object under study. if there is nor crack or cavity in its path, it goes through the object. A detector placed on the other side detects the transmitted wave. A defect present in the path of the wave reflects the wave. Thus, the intensity of the emerging waves falls in the region that is in line with the defect. When this happens, we know that the object has defect inside. Ordinary sound is not used for this application because ordinary sound will bend considerably round the corners of crakes or cavities and will average of the other side at almost full intensity.

(vi) Bats fly in the darkness of night without colliding with other objects by the method of echolocation. Bats emit high frequency ultrasonic squeaks while flying and listen to he echoes produced by the reflection of their squeaks from the objects in their path. From the time taken by the echo to be heard, bats can judge the distance of the object in their path and hence avoid it by changing the direction. Bats search their prey at night by the method of echolocation.

SONAR

 The word ‘SONAR’ stands for ‘Sound Navigation and Ranging’/

(a) Principle of Sonar :

Sonar is an apparatus which is used to find the depth of a sea or to locate the under water things like shoals of fish, enemy submarines etc. Sonar works by sending short bursts of ultrasonic sound from a ship down into sea-water and then picking up the echo produced by the reflection of ultrasonic sound from under-water objects like bottom of sea, shoal of fish, a submarine.

(b) Working of Sonar :

A sonar apparatus consists of two parts :

(i) A transmitter (for emitting ultrasonic waves) and (ii) a receiver (for detecting ultrasonic waves). Now suppose a sonar device is attached to the under-side of a ship and we wan to measure the depth of sea (blow the ship). To do this, the transmitter of sonar is made to emit a pulse of ultrasonic sound with a very high frequency of about 50,000 hertz. This pulse of ultrasonic sound travels down in the sea-water towards the bottom of the sea . When the ultrasonic sound pulse strikes the bottom of the sea, it is reflected back to the ship in the from of an echo. This echo produces an electrical signal in the receiver part of the sonar device. The sonar device measures the time taken by the ultrasonic sound pulse to travel from the ship to the bottom of the sea and back to the ship. Half of this time gives the time taken by the ultrasonic sound to travel from the ship to the bottom of the sea.

Depth of sea =       velocityof sound in sea water x time covered by  the recorder / 2

                          d= vx t/2                                     

 ILLUSTRATION

1.The ultrasonic waves take 4 seconds to travel from the ship to the bottom of the sea and back to the ship. What is the depth of the sea ? (Speed of sound in water = 1500 m/s.)

Sol. The time taken by the ultrasonic sound waves to travels from the ship to the sea-bed and back to the ship is 4 seconds. So, the time taken by the ultrasonic sound to travel from the ship to sea-bed with be half of this time, which is  seconds. This means that the sound takes 2 seconds to travel from the ship to the bottom of the sea.

Now,      Speed =   Distance/ time

 So,           1500 = Distance / 2

And,       Distance = 1500 × 2 m = 3000 m

REASON FOR USING ULTASONIC WAVES IN SONAR

(i) Ultrasonic waves have a very high frequency due to which they can penetrate deep is sea water without being absorbed.

(ii) Ultrasonic waves cannot be confused with the noises, such as the voice of engines of ship. It is because the ultrasonic waves are not perceived by human ear.

THE HUMAN EAR

The ears the sense organs which help us in hearing sound.

(a) Construction of Human Ear :

The ear consists of three compartments : outer ear, middle ear and inner ear. The part of ear which we see outside the head is called outer ear. The outer ear consists of broad part called pinna and about 2 to 3 centimeters long passage called ear canal. At the end of ear canal there is a thin, elastic and circular membrane called ear-drum. The ear-drum is also called tympanum. The outer ear contains air. The middle ear contains three small and delicate bones called hammer, anvil and stirrup. These ear-bones are linked to one another. One end of the bone called hammer is touching the ear-drum and its other end is connected to the second bone called anvil. The other end of anvil is connected to the third bone called stirrup and the free and of stirrup is held against the membrane over the oval window of inner ear. The middle ear also contains air. The lower part of middle ear has a narrow tube called ‘eustachian tube’ going to the throat. Eustachian tube connects the middle ear to throat and ensures that the air pressure inside the middle ear is the same as that on the outside. 

The inner ear has a coiled tube cochlea. One side of cochlea is connected to the middle ear through the elastic membrane over the oval window. The cochlea is filled with a liquid. The liquid present in cochlea contains never cells which are sensitive to sound. The other side of cochlea is connected to auditory nerve which goes into the brain.

(b) Working of Human Ear :

The sound waves (coming from a sound producing body) are collected by the pinna of outer ear. These sound waves pass through the ear canal and fall on the ear-drum. Sound waves consist of compressions (high pressure regions) and rarefactions (low pressure regions). When the compression of sound wave strikes the ear-drum, the pressure on the outside of ear-drum increases and pushes the ere-drum inwards and when the rarefaction of sound wave falls on the ear-drum, the pressure on the outside of ear-drum decreases and it moves outward. Thus, when the sound waves fall on the ear-drum, the ear-drum starts vibrating back and forth rapidly.

The vibrating ear-drum causes a small bone hammer to vibrate. From hammer, vibrations are passed on to the second bone anvil and finally to the third bone stirrup. The vibrating stirrup strikes on the membrane of the oval window and passes its vibrations to the liquid in the cochlea. Due to this, the liquid in the cochlea beings to vibrate. The vibrating liquid of cochlea sets up electrical impulses in the nerve cells present in it. These electrical impulses are carried by auditory nerve to the brain. The brain interprets these electrical impulses as sound and w get the sensation of hearing.

MOTION

MOTION Motion means movement. The motion of an object is perceived when its position changes continuously with respect to some stationary object.

DISTANCE The distance travelled by an object is the length of actual path travelled by the object during the motion.

DISPLACEMENT The displacement of an object is the shortest distance travelled between the initial and final position of the object.

• When final position coincides with the initial position, displacement is 0 but distance is not equal to 0.

• Both, the distance and displacement are measure in meter or cm or km.

• Distance is a scalar quantity having only. Displacement is a vector quantity having both magnitude and direction.

• The distance travelled by an object in motion can never be zero or negative. The displacement can be positive, zero or negative.

INTEXT QUESTIONS

1. A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?

Ans. The farmer takes 40 s to cover 4 × 10 = 40 m. In 2 min and 20 s (140 s), he will cover a distance = 40/40* 140 =140m

Therefore, the farmer completes 140/40= 3.5 rounds (3 complete rounds and a half round) of the field in 2 min and 20 s. That means, after 2 min 20 s, the farmer will be at the opposite end of the starting point.

Now, there can be two extreme cases.

Case I: Starting point is a corner point of the field. In this case, the farmer will be at the diagonally opposite corner of the field after 2 min 20s.

Therefore, the displacement will be equal to the diagonal of the field. Hence, the displacement will be √10² +√10^2 =14.1m

Case II: Starting point is the middle point of any side of the field. In this case the farmer will be at the middle point of the opposite side of the field after 2 min 20 s.

Therefore, the displacement will be equal to the side of the field, i.e., 10 m. For any other starting point, the displacement will be between 14.1 m and 10 m.

2. Which of the following is true for displacement?

(a) It cannot be zero.

(b) Its magnitude is greater than the distance travelled by the object.

Ans. (a) Not true. Displacement can become zero when the initial and final position of the object is the same.

(b) Not true. Displacement is the shortest measurable distance between the initial and final positions of an object. It cannot be greater than the magnitude of the distance travelled by an object. However, sometimes, it may be equal to the distance travelled by the object.

UNIFORM MOTION

A body is said to have a uniform motion if it travels equal distances in equal intervals of time, no matter how small these intervals may be. Eg. A vehicle running at a constant speed of 10m/sec ,will cover equal distances of 10metres every second, so its motion will be uniform.

NON-UNIFORM MOTION

A body is said to have a non- uniform motion if it travels unequal distances in equal intervals of time, no matter how small these intervals may be. Eg. A freely ball from a certain height covers unequal distances in equal intervals of time, so its motion is non uniform.Non uniform motion is also called accelerated motion.

SPEED

Speed of a body is defined as the distance travelled by the body in unit time.

Speed( v )= distance travelled( s)/time taken( t)

Speed is a scalar quantity.

Uniform Speed: When a body travels equal distances in equal intervals of time, the speed of the body is said to be uniform.

Non-uniform Speed: When a body travels unequal distances in equal intervals of time, the speed of the body is said to be non-uniform.

VELOCITY

Velocity of a body is the distance travelled by the body in unit time in a given direction.

Velocity=distance travelled in a given direction /time taken=displacement/time

Velocity is a vector quantity.

Uniform Velocity: When a body travels equal distances in equal intervals of time in a particular direction, the velocity of the body is said to be uniform.

Non-uniform Velocity: When a body travels unequal distances in equal intervals of time in a particular direction, the velocity of the body is said to be non-uniform. Both speed and velocity are measured in m/s or cm/s or km/hr

AVERAGE VELOCITY

Average Velocity: When velocity of a body is changing at a uniform rate, average velocity is given by v_av = Initial velocity(u) + final velocity(v) / 2

INTEXT QUESTIONS

1. Distinguish between speed and velocity.

2. Under what condition(s) is the magnitude of average velocity of an object equal to its average speed?

Ans.

Average speed = Total distance covered / Total time taken

and

Average velocity = Displacement / Total time taken

If the total distance covered by an object is the same as its displacement, then its average speed would be equal to its average velocity.

3. What does the odometer of an automobile measure?

Ans. The odometer of an automobile measures the distance covered by an automobile.

4. What does the path of an object look like when it is in uniform motion?

Ans. An object having uniform motion has a straight line path.

5. During an experiment, a signal from a spaceship reached the ground station in five minutes. What was the distance of the spaceship from the ground station? The signal travels at the speed of light, that is, 3 × 10⁸ m ^s−1.

Ans. Time taken by the signal to reach the ground station from the spaceship

= 5 min = 5 × 60 = 300 s

Speed of the signal = 3 × 10⁸ m/s

Speed = Distance travelled / Time taken

∴Distance travelled = Speed × Time taken = 3 × 10⁸ × 300 = 9 × 10¹⁰ m

Hence, the distance of the spaceship from the ground station is 9 × 10¹⁰ m.

ACCELERATION

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

given by formula:

a = (v - u) / t

It is measured in m/s² or cm/s² or km/hr². Acceleration is a vector quantity.

If the velocity of the body increases with time, the acceleration is positive, and the kind of motion is called accelerated motion. If the velocity of the body decreases with time, the acceleration is negative (retardation), and the motion is called decelerated motion.

Uniform Acceleration: When velocity of the body changes by equal amounts in equal intervals of time in a particular direction, the acceleration of the body is said to be uniform.

Non-uniform Acceleration: When velocity of the body changes by unequal amounts in equal intervals of time in a particular direction, the acceleration of the body is said to be non- uniform.

INTEXT QUESTIONS 

1. When will you say a body is in (i) uniform acceleration? (ii) non-uniform acceleration?

Ans. (i) A body is said to have uniform acceleration if it travels in a straight path in such a way that its velocity changes at a uniform rate, i.e., the velocity of a body increases or decreases by equal amounts in an equal interval of time.

(ii) A body is said to have non-uniform acceleration if it travels in a straight path in such a

way that its velocity changes at a non-uniform rate, i.e., the velocity of a body increases or decreases in unequal amounts in an equal interval of time.

2. A bus decreases its speed from 80 km h−1 to 60 km h−1 in 5 s. Find the acceleration of the bus.

Ans. Initial speed of the bus, u = 80 km/h = 80 * 5/18 = 22.22m / s

Final speed of the bus, v = 60 km/h = 60 * 5/18 = 16.66m / s

Time take to decrease the speed, t = 5 s

Acceleration, a = v - u / t = 16.66 - 22.22 / 5 = -1.12m/s²

Here, the negative sign of acceleration indicates that the velocity of the car is decreasing.

3. A train starting from a railway station and moving with uniform acceleration attains a speed 40 km h−1 in 10 minutes. Find its acceleration.

Ans. Initial velocity of the train, u = 0 (since the train is initially at rest)

Final velocity of the train, v = 40 km/h = 40 * 5/18 = 11.11m / s

Acceleration, a = v - u /t = 11.11 - 0 / 5 = 0.0185m / s²

Time taken, t = 10 min = 10 × 60 = 600 s

Hence, the acceleration of the train is 0.0185 m/s².