Phy IIT Module I Kinematics

8/11/2019 Phy IIT Module I Kinematics

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241321407.doc 1

NEMAT CS

SINGLE ANSWER TYPE QUESTIONS

1. The greatest acceleration or deceleration that a train may have is a. The minimum timein which the train can go from one station to the next at a distance S is

A)aS B)

aS2 C) 2

as D)

a2s

2. A car accelerates from rest at a constant rate for sometime and attains a velocity of

2 m!s. Afterwards it decelerates with a constant rate !2 and comes to a halt. "f thetotal time ta#en is 1s$ the distance travelled %y the car isA) 2m B) 1m C) 1m D) 2m

&. A 'article starts from rest at time t ( and moves on astraight line with an acceleration which varies with time asshown in g. The s'eed of the 'article will %e maximumafter how many seconds

A) *s B) +sC) ,s D) 1s

*. A 'article starts from the 'osition of rest under a constant acceleration. "t travels adistance x in the rst 1 seconds and distance y in the next 2 seconds. ThenA) y ( x B) y ( 2x C) y ( ,x D) y ( *x

-. Due to air a falling %ody faces a resistive force 'ro'ortional to suare of velocity v$conseuently its e/ective downward acceleration is reduced and is given %y a ( g 0 #v 2

where # ( .2m01. The terminal velocity of the falling %ody isA) *m!s B) m!s C) .,m!s D) ,m!s

+. A %alloon is rising with a constant acceleration of 2m!s2. At a certain instant when the%alloon was moving with a velocity of *m!s$ a stone was dro''ed from it in a regionwhere g ( 1m!s2. The velocity and acceleration of stone as it comes out from the%alloon are res'ectively.A) $ 1m!s2 B) *m!s$ ,m!s2 C) *m!s$ 12m!s2 D) *m!s$ 1m!s2

. A %ody is 'ro3ected vertically u'wards. "f t1and t2%e the times at which it is at height ha%ove the 'oint of 'ro3ection while ascending and descending res'ectively$ then h is

A) 21ttg2

1B) g t1t2 C) 2 g t1t2 D) * g t1t2

,. 4rom a 2m high tower one %all is thrown u'ward with s'eed of 1m!s and another isthrown vertically downward at the same s'eed simultaneously. The time di/erence oftheir reaching the ground will %e 5ta#e g ( 1m!s2)A) 12s B) +s C) 2s D) 1s

. A stone is thrown vertically u' from the to' of a tower with some initial velocity and it

arrives on the ground after t1seconds. 6ow if the same stone is thrown vertically downfrom the to' of the same tower with the same initial velocity$ it arrives on ground aftert2seconds. 7ow much time will the stone ta#e to reach the ground if it is dro''ed fromthe same tower 8

A)2

tt 21 + B)2

tt 21 C) 21 tt + D) 21tt

1. Two 'articles A and B are connected %y a rigid rod AB. The rodslides on 'er'endicular rails as shown in g. The velocity of A tothe left is 1m!s. 9hat is velocity of B when ( +8A) 1m!sB) -.,m!sC) 1.&m!sD) .,m!s

11. Two 'articles A and B start from the same 'oint and slide downthrough straight smooth 'lanes inclined at &and +to the vertical and in the samevertical 'lane and on the same side of vertical drawn from the starting 'oint. Theacceleration of B with res'ect to A isA) g!2 in vertical direction B) g 2/3 at *-to vertical

C) g! 3 at +to vertical D) g in vertical direction12. A 'article : moving with a constant velocity u crosses a 'oint ;. At the same instant

another 'article 4 starts from rest from ; with a constant acceleration a. The maximumse'aration %etween them %efore they meet is


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241321407.doc 2

A)a2

u 2B)

a

u2C)

a

u2 2

D)a4

u 2

1&. A %ird


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241321407.doc 32&. A 'article starts from the origin of coordinates at time t ( and moves in the xy 'lane

with a constant acceleration in the y0direction. "ts euation of motion is y (x2. "tsvelocity com'onent in the x0direction is

A) varia%le B)2

C)

2D)

2

2*. "n the gure $ the 'ulley moves to the right with a constants'eed u. The downward s'eed of A is vA$ and the s'eed of B to

the right is vB.A) vB( vAB) vB( u = vAC) vB= u ( vAD) The two %loc#s have accelerations of the same magnitude

2-. The hori@ontal range of a 'ro3ectile is and the maximum height attained %y it is 7. Astrong wind now %egins to %low in the direction of the motion of the 'ro3ectile$ giving ita constant hori@ontal acceleration ( g!2. Ender the same conditions of 'ro3ection$ thehori@ontal range of the 'ro3ectile will now %e

A) =2

HB) = 7 C) =

2

H3D) = 27

2+. A 'article moves int he xy 'lane with a constant acceleration g in the negative y0

direction. "ts euation of motion is y ( ax 0 %x2$ where a and % are constants. 9hich ofthe following are correct 8A) The x0com'onent of its velocity is constant

B) at the origin$ the y0com'onent of its velocity is ab2

g

C) At the origin$ its velocity ma#es an angle tan 015a) with the x0axis.D) the 'article moves exactly li#e a 'ro3ectile.

2. Two %odies are 'ro3ected simultaneously from the same 'oint$ in the same vertical'lane$ one towards east and other towards west with velocities , ms01 and 2 ms01

res'ectively. The time at which their velocities are 'er'endicular to each other isA) 2!- s B) -!2s C) 1!- s D) - s

2,. A train starts from station A with uniform acceleration for some distance and thengoes with uniform retardation for some more distance to come to rest at station B. Thedistance %etween station A and B is * #m and the train ta#es * minute to com'lete this3ourney. "f and are in #m 5min)02then

A) 211=

+

B)4

11=

+

C) 2111

=

+ D) 4

111=

+

2. Two stones are 'ro3ected so as to reach the same distance from the 'oint of 'ro3ection

on a hori@ontal surface. The maximum height reached %y one exceeds the other %y anamount eual to half the sum of the heights attained %y them. Then the angles of'ro3ection for the stones areA) *-$ 1&- B) $ C) &$ + D) 2$

&. A mar%le starts falling from rest on a smooth inclined 'lane forming an angle withhori@ontal. After covering distance >h> the %all re%ound o/ the 'lane. The distance fromthe im'act 'oint where the %all re%ounds for second time isA) ,h cos B) ,h sin C) 2h tan D) *h sin

&1. The driver of a train moving with a s'eed v1sights another train at a distance d$ aheadof him moving in the same direction with a slower s'eed v 2. 7e a''lies the %rea#s andgives a constant de0acceleration >a> to his train. 4or no collision$ d is

A) (( )

a2

vv 2

21 B) F ( )a2

vv 221 C) G ( )

a2

vv 221 D) G

a2

vv 21

&2. "n the case of a moving %ody$ 'ic# the correct statementA) if s'eed changes with change in direction$ velocity does not changeB) if velocity changes$ s'eed may or may not change %ut acceleration does changeC) if velocity changes$ s'eed also changes with same accelerationD) if s'eed changes without change in direction$ the velocity may remain constant.

&&. article 1 is in one dimensional motion with uniform velocity whereas 'article 2 isaccelerating in a straight line. The gra'h re'resenting 'ath of 2 with res'ect to 1 is

A) B) C) D)


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241321407.doc 4&*. erson A wal#ing along a road at &ms01sees another 'erson B wal#ing on another road

at right angles to his road. Helocity of B is *ms01when he is 1m o/. They are nearest toeach other when 'erson A has covered a distance ofA) &.+m B) ,m C) +.&m D).,m

&-. The given gra'h shows the variation of velocity with dis'lacement.9hich one of the gra'hs given %elow correctly re'resents thevariation of acceleration with dis'lacement.

A) B) C) D)

&+. Helocity and acceleration of a 'article at some instant of time are ( j4i3v += m!s and( j8i6a += m!s2res'ectively. At the same instant 'article is at origin. Iaximum x0co0

ordinate of 'article will %eA) 1.-m B) .-m C) 2.2-m D) *.m

&. v2versus s0gra'h of a 'article moving in a straight line is as shown in gure. 4rom thegra'h some conclusions are drawn. State which statement is wrong A) the given gra'h shows a uniformly accelerated motion.B) initial velocity of 'article is @eroC) corres'onding s0t gra'h will %e a 'ara%olaD) none of the a%ove

&,. a0t gra'h for a 'article moving in a straight line is as shown ingure. Change in velocity of the 'article from t( to t(+s is A) 1m!s B) *m!sC) 12m!s D) ,m!s

&. S'eed time gra'h of two cars A and B a''roaching towardseach other is shown in gure. "nitial distance %etween them is+m. The two cars will cross each other after time.A) 2sec B) &secC) 1.-sec D) 2 sec

*. The 'osition of a 'article along x0axis at time t is given %y x ( 2= t 0 &t2. The dis'lacement and the distance travelled in theinterval t ( to t ( 1 are res'ectivelyA) 2$ 2 B) 02$ 2.- C) $ 2 D) 02$ 2.1+

*1. A %ody dro''ed from the to' of the tower covers a distance x in the last second of its3ourney$ where x is the distance covered in rst second. 7ow much time does it ta#e toreach the ground 8A) &s B) *s C) -s D) +s

*2. A %ody is 'ro3ected with a velocity u. "t 'asses through a certain 'oint a%ove the groundafter t1 sec. The time interval after which the %ody 'asses through the same 'ointduring the return 3ourney is

A)

21t

g

uB) 2

1t

g

uC) &

1

2

t

g

uD) &

12

2

t

g

u

*&. The area of the acceleration0dis'lacement curve of a %ody gives A) im'ulse B) change in momentum 'er unit massC) change in JK 'er unit mass D) total change in energy

**. A %ody thrown vertically u' from the ground 'asses the height 1.2m twice at aninterval of 1s. 9hat was its initial velocity 5g ( 1m!s 2)A) -2m!s B) 2+ m!s C) &- m!s D) + m!s

*-. The acceleration time gra'h of a 'article moving along astraight line is as shown in gure. At what time the 'articleacuires its initial velocity 8A) 12sB) -s


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241321407.doc 5C) ,sD) 1+s


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241321407.doc 6*+. A gra'h %etween the suare of the velocity of a 'article

and the distance s moved %y the 'article is shown in thegure. The acceleration of the 'article in #ilometre 'erhour suare is A) 22-B) 22-C) 022-D) 022-

*. A 'article starts from rest and traverses a distance lwith uniform acceleration$ thenmoves uniformly over a further distance 2land nally comes to rest after moving afurther distance &lunder uniform retardation. Assuming entire motion to %e rectilinearmotion the ratio of average s'eed over the 3ourney to the maximum s'eed on its way isA) 1!- B) 2!- C) &!- D) *!-

*,. An insect crawls a distance of *m along north in 1 seconds and then a distance of &malong east in - seconds. The average velocity of the insect is A) !1- m!sec B) 1!- m!sec C) 1!& m!sec D) *!- m!sec

*. A 'article returns to the starting 'oint after 1s. "f the rate of change of velocity during

the motion is constant in magnitude$ then its location after seconds will %e same asthat after A) 1 second B) 2 seconds C) & seconds *) * second

-. Two stones are thrown u' simultaneously with initial s'eeds of u1andu25u2F u1). Theyhit the ground after +s and 1s res'ectively. 9hich gra'h in gure correctly re'resentsthe time variation of x ( 5x20 x1)$ the relative 'osition of the second stone with res'ectto the rst u'to t ( 1s 8 Assume that the stones do not re%ound after hitting theground.

A) B) C) D)-1. 4igure shows the 'osition0time 5x0t) gra'h of the motion of two

%oys A and B returning from their school ; to their homes and Lres'ectively. 9hich of the following statements is true 8A) A wal#s faster than BB) Both A and B reach home at the same timeC) B starts for home earlier than AD) A overta#es B on his way to home

-2. Two 'articles and L simultaneously start moving from 'oint Awith velocities 1-m!s and 2m!s res'ectively. The two 'articles move with accelerationseual in magnitude %ut o''osite in direction. 9hen overta#es L at B then its velocity

is &m!s. The velocity of L at 'oint B will %eA) &m!s B) -m!s C) 2m!s D) 1-m!s

-&. Met aandv denote the velocity and acceleration res'ectively of a 'article in onedimensional motionA) the s'eed of the 'article decreases when 0av C) the s'eed of the 'article increases when 0av =D) the s'eed of the 'article decreases when av > is travelling with a velocity of 0v

hori@ontally from the left as shown in the gure. "t isconstrained to move along a smooth trac#. At >A> itcan continue to travel along one of the four 'aths$

[ ] ,,, $ as indicated in the diagram. "t is giventhat all the four 'aths$ vi@. ,, and are in thesame vertical 'lane. All the four 'aths 3oin at >B> afterwhich the o%3ect continuous moving hori@ontally. Thetime ta#en to traverse the hori@ontal distance AB along the 'ath "" is >T>. A detail ofthe four di/erent 'aths is given as is the hori@ontal 'ath.

is a >hill> 'ath. is a shallow valley which can %e assumed to have the same length as the

hori@ontal 'ath >AB>. is a dee' valley 'ath$ with a minimum de'th >7>.

Assume the total energy 5K) is to mass 5m) ratio of the 'article as "2/" .

&


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241321407.doc 181+. The ratio of the velocity of the 'article at a height of >h> on and the velocity of the

'article at a de'th of >h> on is

A)

+

gh

gh

2

2

B)

+

gh

gh

2

2

C)

2/1

2

2

+

gh

gh

D)

2/1

2

2

+

gh

gh

1. "f the time ta#en %y the o%3ect to travel from A to B along is t $ then

A) Ttt == B) Ttt => C) Ttt =< D) cannot %e 'redicted

1,. "f the time ta#en %y the o%3ect to travel from A to B along is t

$ then A) Ttt == B) Ttt => C) Ttt =< D) cannot %e 'redicted

1. "f the time ta#en %y the o%3ect to travel from A to B along is t $ then

A) Ttt == B) Ttt => C) Ttt =< D) cannot %e 'redicted2. "f we a''roximate the time ta#en to travel from A to B along the dee' 'ath "" %y the

time ta#en for a vertical return 'ath of de'th >7>$ i.e.$ from A and %ac# to A$ %y assumingthe initial velocity to %e negligi%le as com'ared with that for the ma3or 'ortion of the'ath$ then the total time ta#en is

A)g

H2B)

g

H4C)

g

H8D) T

Passage I (Q.No: !1 to !3)A 'oint moves rectilinearly in one direction. 4igureshows the distance s traversed %y the 'oint as a functionof time t. Esing this gra'h$ answer the followinguestions.

21. The average velocity of the 'oint during the time ofmotion isA) 1 cm!s B) 1- cm!sC) 2 cm!s D) 2- cm!s

22. The maximum velocity isA) 1- cm!s B) 2 cm!s

C) 2- cm!s D) & cm!s2&. The time moment 0t at which the instantaneous velocity is eual to the mean velocity

averaged over the rst 0t second is

A) 1s B) 1+s C) 1,s D) 2s

Passage II (Q.NO !4 to !$):Two 'articles are initially located at 'oints A and B adistance d a'art as show in gure. They startmoving at time t ( such that the velocity u of B isalways along the hori@ontal direction and velocity vof A is continually aimed at B as shown in gure.At

time t ( $ u is 'er'endicular to v.2*. A%out the velocities u and v$ we can say thatA) %oth the velocities are constantB) %oth the velocities are changingC) the velocity u is constant while the velocity v ischangingD) the velocity v is constant while the velocity u is changing

2-. The relative velocity of a''roach of A towards B isA) 5v 0 u cos ) B) 5v = u cos) C) 5u 0 v cos) D) 5u = v cos )

2+. The 'articles A and B will meet after a time

A)22

uv

vd

+B)

( )22 uvvd

C)

( )vd

uv 22 +

D)( )

vd

uv 22

Passage & III (Q.No: !7 to !') :4igure shows the velocity time gra'h of a 'article moving along a straight line.Answer the following uestions.

2. The region in which the rate of change of velocityof the 'article is maximum.A) to 2 s B) 2 to * sC) * to + s D) + to , s

2,. The 'article comes to rest at timeA) sec B) *.+ secC) - sec D) , sec

2. The maximum dis'lacement of 'article is


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241321407.doc 1!A) &&.& m B) 2.2 m C) 2+.+ m D) @ero

PASSAGE & I (Q.No: 3% to 33):;n the %an# of a river two swimmers made achallenge as who will reach the 'oint B on the other%an# early8 So %oth of them start from 'oint >A> onone %an# of the river to reach the winning 'oint B on

the other %an#$ lying directly o''osite to 'oint A.The stream velocity was #nown to %e 2 #m!hr andthe velocity of %oth the swimmers in still water was2.- #m!hr. Both of them follow di/erent 'aths toreach 'oint B the swimmer >S1> crosses the river along straight line AB$ while the otherswimmer >S2> swims at rights to the stream and then wal#s the distance which he has%een carried away %y the stream to go to the 'oint >B>. Assume the velocity 5uniform)of his wal#ing as 52!&) #m!hr and the width of the river as >9>.

&. The value of angle "" shown in the gure isA) cos015*!-) B) cos015&!*) C) sin015*!-) D) sin015&!*)

&1. The value of angle "" shown in the gure is A) sin015*!-) B) cos015*!-) C) tan015*!-) D) data insuQcient

&2. Iatch column " with column "" in reference to the 'assage.Column " Column ""

" Time for S1 to reachB

5A)

5

4W

"" Time for S2 to reachC

5B)

5

6W

""" Drift >x> for S2 5C)

3

2W

"H Time for S2 to reachB from C

5D)

15

8W

H Di/erence in time$t $ for S1and S2 to

reach B

5K)

52W

A) "0C$ ""0K$ """0A$ "H0B$H0D B) "0A$ ""0B$ """0D$"H0C$ H0KC) "0K$ ""0C$ """0B$ "H0D$ H0A D) "0B$ ""0A$ """0D$ "H0C$ H0K

&&. 9hat should %e the velocity 5assume uniform) of wal#ing of swimmer >S2> such that %oththe swimmers reach at the 'oint B simultaneously8A) 1.2 #m!hr B) 2. #m!hr C) & #m!hr D) needs moreinformation

*ULTIPLE *AT+,ING TYPE QUESTIONS:

1. Iatch the followingList - I L-st & IIa) ange ( height 5Iax) e) acceleration 'er'endicular

to velocity%) 4or ( *-$ at the highest'oint

f) (g17

8

c) y ( 'x = x2g) Jmin(

2

15Jmax)

d) At t ( T!2 5for 'ro3ectile)h) ( Tan

01

5*)i)

1g

2#

2 +=

u

2. Iatch the followingList - I L-st & IIa) one dim. motion e) motion of one 'ro3ectile w.r.t another 'ro3ectile%) for no airresistance

f) time of ascent ( Time of decent for a vertically'ro3ected u' %ody

c) for 'ro3ectile 7 ( g) T ( 2u!g$ for a %ody vertically 'ro3ected u'


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241321407.doc 20!*

d) ange (g

u 2 i) ( *-

&. Iatch the followingList - I L-st & IIa) v0 t gra'h e) Area gives dis'lacement%) x 0 t 0 gra'h f) slo'e gives velocityc) a 0 t gra'h g) slo'e gives accelerationd) a x h) Area gives change in velocity

h) slo'e of v 0 x gra'h isconstantt) non uniform acceleration

*. Iatch the followingList - I L-st & IIa) Iagnitude of acceleration isconstant

e) uniform circular motion

%) tangential acceleration is @ero f) non0uniform circular motionc) s'eed is constant g) 'ro3ectile motiond) angle %etween radial accelerationand velocity is

h) accelerated straight linemotion

O O O


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241321407.doc 21e/

S-0ge A0s2e T/e Q5est-o0s:

1. -2. =&. . 1. =11. 1. >1,. =1. -2. -21. =22. =2&. >2*. =,>2-.

>2+.

Phy IIT Module I Kinematics

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