nUNIT L

IXTRODUCTION

o Origin is a fixed point with respect to which the3.-rsition of any object changes.

r Distance is the actual length of the path covered:r a body during the whole joumey, without takingIro consideration its direction. It is a scalar quan-:il'.

. Displacement is the distance in a particular di-:n-tion. It is a vector quantity. It must be kep in:nind that the distance travelled is always positive.tJn the other hand, displacement may be positive,regative or zero,

o Difference between distance and displacementDistance travelled is always greater than or equal:.. the displacement. On the other hand, displace-

=rent is always less than or equal to the distanceravelled.

r Condition under which distance and displace-ment become same\\hen a body moves along a straight line in a posi-:ive direction, then its displacement and the dis-'-ance travelled are equal and have the same sign.

r Speed is the rate ofchange ofdistance..

-{verage speed is defined as the total distanceravelled, divided by the total time taken.

r Initial speed is that speed with which a body starts:s motion in the beginning. It is denoted by rz.It is zero whenever a body starts from rest.

Final speed is that speed which is acquired by thebody after its start. It is denoted by v. When abody finally comes to rest its final speed is zero.Scalar quantities are those which have magni-tudeonly,but,vectorquantitieshavebothmagni-tude and. direction. For example, the amount oftime and speed are scalar quantities because theyhave only magnitude, but acceleration and forceare vector quantities because they have magnitudeand direction. The magnitude of a vector is calledmodulus of the vector.When a body covers unequal distances in equalintervals of time, or its direction changes or bothchange, its velocity is said to be variable.When a body travels equal distances in equalintervals of time, however small the intervals oftime may be, its velocity is said to be unifurm.The rate of change of angular displacement iscalled angul ar v e I o city.Acceleration of a body is defined as the rate ofchange of velocity. Acceleration has both magni-tude and direction, hence it is a vector quantity.The rate ofchange ofangular velocity is calledangalar accelerstion.Centripetal accelerationIf a body is moving along the circumference of acircle, then the acceleration produced is directedtowards the centre of the circle. This accelerationis called centripetal acceleration. Force due to

II.A.1O Study Package for NTSE

centripetal acceleration, acting towards the centre,is called the centripetalforce.

o RetardationWhen the final ,speed of a body is less than itsinitial speed, the body is said to be retarding.Retardation can also be expressed as accelerationwitlr a minus sign.

r Uniferm speedWhenever a body colers equal distances in equalintervals of time, however small these intervalsof time may be, then the speed is said to beuniform.

o Uniform accelerationIf velocity increases by equal amounts in equalintervals of time in a straight line, however smallthe intervals of time may be, the body is said tohave uniform acceleration.

e Graphs and their usesCraftrs proVide much more information thanobservations recorded in tabular form. From thegraphs one can find out even those values whichare not given in the data. The position of themoving body canrbe easily located at any instantof time. One can also come to know whether thebody is moving with uniform speed or not. To plota graph, always take the independent quantity onthe x-axis and the dependent on the y-axis.

o Slope ofthe graphs(i) The slope ofthe distance-time graph gives the

speed of thei moiing body. :(ii) The distance travelled by a body can be

obtained by deteimining'the'aiea urtder thespeed-time graph.

(iii) The slope ofthe velocity-time graph gives theacceleration of the moving body-

(iv) By plotting the distance-time graph of twobodies, one can find out when and:where thetwo bodies cross each other.

Tick (/) thecorrect'thoice amongst the following:I . Unit of acceleration is

2. A body goes from A to B with a velocity of20m!s and comes back from B to A with avelocity of 30 m/s. The average velocity of thebody during the whole journey is

3. A body covers half the distance with a speedof 2b m/s and the other half with a speed of

: 30 m/s. The average velocity ofthe body duringthe whole journey is(a) zero (b) 24 mls(c) 25 m/s (d) none of these

(a) zero'(c) 24mls

(a) m/s2, m/s(c) rnls, m/s

(a) 0.21 cm/s(c) 21.0 cm/s

(b) 25 m/s(d) none ofthese

(b) 2.1cm/s(d) none ofthese

.

4.

5.

In the equation of motion, S --

ut + U2 aP, Sstands for(a) distance in I seconds(b) maximum height reached(c) distance in the P second(d) none oftheseChoose the- wrong statement.(a) retardation is a vectoi quantity(b) acceleration due to gravity is a vector

quantity(c) average speed is a vector quantrtyIn the equation of molion, x : at + bP, thg untofa and D are respectively

(b) m/s, m/s2(d) none of these

A body is thrown up with an initial velobity rand covers a maximum height of 4 then ft isequal to

2u\a) ;

(c) 2ug ({) none of these..8. The second's hand of a watch is 2 cm long.

The speed of the tip of this hand is

7.

(b) 2s

9. A body is thrown vertically upwards andlisqto a height of l0 m. The velocity with whichthe body was tfuown upwards is (g : 9.8 m/s1

(b) 20 mis(d) none ofthese

10. In question number nine the time taken by,thebody to reach the highest point is

(a) l0 rn/s(c) 14 m/s

(a) m/s(c) m/s2 O)

ms(d) none ofthese

Motion II.A.11

11. If the time-displacement graph of a particle isparallel to the time-axis, the velocity of theparticle is(a) infinity(b) unity(c) equal to acceleration ofthe body(d) zeroVelocity-time gaphAB (Fig. 2.1) shows thatthebody has(a) a uniform acceleration(b) a non-uniform retardation(c) uniform speed(d) initial velocity OA atd is moving with

uniform retardation

;;,Velocitytime graph,4B (Fig. 2.2) shows that thebody has(a) uniform acceleration(b) uniform retardation(c) unifonn velocity throughout its motion and

has zero initial velocity(d) none ofthese

----->lFig" 2.2

14. The distance havelled by a freely falling bodyis proportional to

(a) the rnass of the body(b) the square ofthe acceleration due to graviry(c) the square of the time of fall(d) the time of fall

15. The rate of change of dispiacement with timeis

(a) 1.43 s(c) 1.24 s ft) a.ls(d) none ofthese

12.16. A body strikes the floor vertically with a

velocity a and rebounds at the same speed. Thechange in speed would be

(b) 3u(d) zero

t7. The moon is 4 x 108 m from the earth. A radarsignal transmitted from the earth will reach themoon in about

(a) speed(c) retardation

(b) acceleration(d) velocity

(b) 1.3 s(d) 0.70 s

(b) B(d) none

(b) x.: x2(d) none ofthese

(b) kmis(d) mmis

(a) u(c) 2u

(.a) 5.2 s(c) 2.6 s

18" A arrd B are arguing about uniform acceleration.I states that acceleration means "the longer yougo." B states that acceleration means "thefurther you go." Who is right?

13.

19. A particle experiences constant acceleration for20 s after starting from rest. If it travels adistanceXl, in the first 10 s and distanceX2, inthe remaining l0 s, then which of the followingis true?(a) x, :2x,(c) ,x, :3x,

(b) 8 m/s(d) 6 m/s

(b) 600m(d) 200 m

la) A(c) both

(a) m/s(c) cm/s

20. If a trolley starts from rest with an accelerationof 2 mlsz, the velocity of the body after 4 swould be{a) 2 mls(c) 4 m/s

21 . A train passes over a 400 m long bridge. Ifthespeed of the train is 30 mis and the train takes20 s to cross the bridge, then the length ofthetrain is(a) 400m(c) 800 m

22. The SI unit for the average velocity is

*

fr:t

II.A.12 Study Package for NTSE

24. A fiain 50 m long passes over a bridge at avelocity of 30 km/h. If it takes 36 s to cross thebridge, the length of the bridge will be

23. The SI rurit for the resultant velocity is (c) Velocity first decreases then increases(d) Nothing can be decidedFrom Question29,we can say that(a) the average speed is 40 km/h(b) the average velocity is 40 km/h(c) the average speed is 80 km,4r(d) the average velocity is 80 km/hA stone tied to a string is whirled in a circle.As it is revolving, the rope suddenly breaks.Then(a) the stone flies off tangentiallyO) the stone moves radially inward(c) the stone moves radially outward(d) the motion of the stone depends upon its

velocityIn the following graph (Fig. 2.q of displace-ment versus time,(a) the body is at rest(b) the body has some initial speed(c) the body moves with constant speed(d) the body moves with constant velocity

---------+- TimeFig.2.4

34. Figure 2.5 shows the displacement-time graphs(a) and (b) for a body moving in a straight pathdrawn on the same scales. Then

Fig.2.5

(a) m/s(c) cm/s

(a) 100m(c) 250 m

(b) lcrls(d) min/s

(b) 200m(d) 300 m

31.

32.25. The SI unit for angular velocity is

(a) mis (b) rad(c) radls (d) m/rad

26. N kgr is lhe unit ol(a) retardation(b) acceleration(c) rate ofchange ofvelocity(d) all the aboveA ball is thrown up with a certain velocity. Itattains a height of 40 m and comes back to thethrower. Then the(a) total distance covered bf it is 40 m(b) total displacement covered by it is 80 m(c) total displacement is zero(d) total distance covered by it is zeroThe acceleration ofa body projected upwardswith a certain velocity is(a) 9.8 m/s2 (b)

-9.8 m/s2(c) zero (d) insufficient data29. A driver is driving his car along a road as shown

in Fig. 2.3. The driver makes sure that thespeedometer reads exactly 40 km/h. What hap-pens to the speed of the car fuam P to Q?(a) Speed remains constant(b) Speed first increases then decreases(c) Speed first decreases then increases(d) Nothing can be decided

Fig"2.330. In the above question, what happens to the

velocity of the car from P to Q?(a) Velocity remains constant(b) Velocity first increases then decreases

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28.

EoEoo(uo".9o+

II.A.13

.r ) slope of line in (a) is greater than the slopeof line in (b)

: t slope ofline in (b) is greater than the slopeof line in (a)

: t slope of line in (a) is equal to the slope ofline in (b)

;t nothing can be said about the slopes.: tbilows from Question 34, that the velocity.:i case of (b) is.r ) more than the velocity in case of (a)r) less than the velocity in case of(a)c t equal to the velocity in case of(a)d; square ofthe velocity in case of(a)

In Fig. 2.6, BCrepresents a body moving,a) backward with uniform velocity,b) forward with uniform velocityr c ) backward with non-uniform velocity,d) forward with non-uniform velocity

O --->- TimeFig.2.6

InFig.2.7 , the velocity of the body at A is

(c) decreases between points I and B(d) is zero throughout

39. A body moving along a circuiar path has(a) a constant speed(b) a constant velocity(c) no tangential velocity(d) no radial acceleration

40. In Fig. 2.8(a) retardation is uniform(b) velocity is decreasing with time(c) beyond M,thebody has negative velocity(d) ali the above are incorrect

Fig.2.8A body whose speed in aparticular direction isconstant(a) must be accelerating(b) must be retarding(c) has a constant velocil.y(d) all the aboveThe velocity of a particle increases from ez to vin a time r during which it covers a distances S.Ifthe particle has a uniform acceleration, u..hichone of the follow'ing equations does not appl3,to the motion?

(a) 2S--{v+u)t {b) a:

(c) y2: u2 2as (d) s- (,.)r),43. A body has an acceleration of

-4 ms-2. lVhatis its retardation?(a)

-4 ms2(b) 4 ms-2(c) Zero(d) nothing can be decided

a-9c)

AI

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41.

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42.(a) zero1c) maximum

(b) unity(d) infinite

v-ut

Rig.2.7In the above question, the velocity(a) increases between points O andl(b) increases between points I and B

II.A.14

44. A cyclist moves from a,certain pointXand goesround a circle of radius 'i' and reaehes I,exactly at the other side of the pointX, as shownin Fig. 2.9. The displacernent ofthe cyclist wouldbe(a) nr(c) 2r

Bte.2.9

In the dbofe problem, the distance covered bythe cyclist would be(a) nr (b) 2 nr(c) 2r (d) 2 nlrWhich ofthe following relations represents therelationship between the average speed, timeand distance correctly?(a) Average speed : distance x time^\ ^ , totaldistance(b) Average speed:(c) rime = **u -n"::tl;lfrL*(d) Distance = average speed

-,timeWhen a graph between two physical quantitiesis a straight line, the two qtihntities arei(a) both constant(b) independent of each other(c) directlyproportional(d) inversely proportionalA man walks 8 m towards East and then 6 mtowards Norttr. His magnitude of displacementis(a) 10m(c) 2m @)

1am(d) zero

49. Area under a velocity-time graph.gives(a) the time takenbya moving object(b) the distance tavelled by a moving object

Study Package for

(c) the acceleration ofrnoving object(d) the retardation of a moving object

50. A player completes a circular path of radiuein 40 s. At the end of 2 minutes 20displacement will be

(b) 2 nr(d) 2nlr

(p) 2,(c) 7 ttr

(a) speed(c) energy

(b) 2.nr(d),zero

(b) distaaoe(d) average velocity

(b) m/s2(d) N/s

(b) 102(d) tO*t

(b) negative(d) infrnite

51, Whichof,the following physical quantitiesdifferent from others?

9. Which of the following physical quantitiesdifferent ftom others?(a) displacement (b) velocity(c) force ''(d) kinetie energy

53. The speed of a body desuibing its motion b(a) direction (b) state(c) type (d) rapidity

54. The unit for the rate of change ofvelocitybe45.

46.

(a)(c)

(a) unity(c) zero

m/sNs

55. The velocity-time graph for a body withuniform motion is a(a) straight line(b) shaight line parallel to x-axis(c) straight line parallel to y:axis(d) curved line

56. The ratio of SI units to CGS units of1S

(a) 10r(c) 10

58.

59.

47.

48.

57. The physical quantity corresponding to the r&of change of displacement is(a) speed (b) velocity(c) acceleration (d) retardationThe velocity of a body at rgst is always

When the distance anobject travels is directlyproportional to the length of tirne, it is said totravel with(a'1 zercvelocity(b) constant speed(c) const?rnt acceleration(d) uniform velocity

II.A.15

In the follorving speed-time graph (Fig.2.l0),the shaded portion gives(a) distance travelled(b) average speed(c) average velocity(d) displacernent travelied

ot2t----->- Time

Fig. 2.10-\ car increases its speed from 20 kmA to 50il 10 seconds. Its acceleration is

lo?xk

62. If the velocity of a body does not change withtime, its acceleration is

(b) 3 ms-2(d) none ofthese

(a) zero(c) unity

l. (c) 2. (a)6. (b) 7. (a)

11. (d) t2. (d)16. (d) 17. (b)21. (d) 22. (a)26. (d) 27. (c)31. (a) 32. (a)36. (a) 37. (a)41. (c) a2. @)46. (b) a7. @)51. (d) s2. (d)56. (b) s7. (b)61. (d) 62. (a)

(b) infinite(d) none ofthese

3. (b) 4. (a) s. (c)8. (a) e. (c) 10. (a)

13. (d) la. (c) ls. (d)18. (c) le. (d) 20. (b)23. (a) 2a. @) 25. (c)28. (b) 2e. (a) 30. (a)33. (a) 3a. @) 3s. (b)38. (b) 3e. (a) 40. (d)43. (b) aa. @) as. @)48. (a) 4e. (b) s0. (a)s3. (d) 54. (b) s5. (d)s8. (c) 59. (b) 60. (a)

ia) 30 ms-2rc) 18 ms-2

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