RECTILINEAR MOTION. Contents. Theory Exercise Exercise Exercise Exercise Answer Key

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1 RECTILINEAR MOTION Conens Topic Page No. Theory Exercise Exercise Exercise Exercise Answer Key 1 - Syllabus Kinemaics in one dimension. Name : Conac No. ARRIDE LEARNING ONLINE E-LEARNING ACADEMY A-479 indra Vihar, Koa Rajashan Conac No

2 RECTILINEAR MOTION KEY CONCEPTS 1. = ds d THINGS TO REMEMBER : ; a = d d = d ds where he symbols hae heir usual meaning. ; s = ò d ; = ò a d ; = ò a ds. The equaions of moion for a body moing in sraigh line wih uniform acceleraion, are (i) = u + a (ii) s = æu + ö a a ç = u + = - è ø (iii) ² = u² + as (i) s n = u + 1 a ( n - 1) () æ + u ö S = ç è ø 3. If a body is hrown erically up wih a elociy u in he uniform graiaional field hen (neglecing air resisance) : (i) Maximum heigh aained H = u g (ii) Time of ascen = ime of descen = u g (iii) Toal ime of fligh = u g (i) Velociy of fall a he poin of projecion = u downwards 4. KINEMATIC GRAPH : Slope of he displacemen ime graph a any paricular ime gies he magniude of he insananeous elociy a ha paricular ime. Slope of he - graph will gie he magniude of he insananeous acceleraion. The area beween he - graph, he ime axis and he ordinaes ereced a he beginning & end of ime ineral considered will represen he oal displacemen of he body. A-479 Indra Vihar, Koa Rajashan Page No. # 1

3 PART - I : OBJECTIVE QUESTIONS * Marked Quesions are haing more han one correc opion. Secion : Disance and Displacemen A-1. A man walks 3m in eas direcion and hen 4m in norh direcion. Disance coered and he displacemen coered by man. 7m, 6m (B) 7m, 5m (C) 7m, 1m (D) 7m, 7m A-. A car sars from P and follows he pah as shown in figure. Finally car sops a R. Disance raelled and 11 displacemen of he car if a = 7 m, b = 8 m and r = m? [Take p = ] p 7 48m, 36m (B) 48m, 4m (C) 48m, 3m (D) 48m, 40m Secion : (B) Aerage speed and aerage elociy B-1. A car raels from A o B a a speed of 0 km h 1 and reurns a a speed of 30 km h 1. The aerage speed of he car for he whole journey is : 5 km h 1 (B) 4 km h 1 (C) 5 km h 1 (D) 50 km h 1 B-*. B-3.* Consider he moion of he ip of he minue hand of a clock. In one hour he displacemen is zero (B) he disance coered is zero (C) he aerage speed is zero (D) he aerage elociy is zero A person raelling on a sraigh line wihou changing direcion moes wih a uniform speed 1 for half disance and nex half disance he coers wih uniform speed. The aerage speed is gien by 1 = (B) = (C) 1 1 = + (D) 1 1 = B-4. A body coers firs 3 1 par of is journey wih a elociy of m/s, nex 3 1 par wih a elociy of 3 m/s and res of he journey wih a elociy 6m/s. The aerage elociy of he body will be 3 m/s (B) 3 11 m/s (C) 3 8 m/s (D) 3 4 m/s Secion : (C)Equaions of moion and moion under graiy C-1. The disance raelled by a paricle is proporional o he squares of ime, hen he paricle raels wih Uniform acceleraion (B) Uniform elociy (C) Increasing acceleraion (D) Decreasing elociy C-. A sone is released from an eleaor going up wih an acceleraion a and speed u. The acceleraion and speed of he sone jus afer he release is a upward, zero (B) (g-a) upward, u (C) (g-a) downward, zero (D) g downward, u A-479 Indra Vihar, Koa Rajashan Page No. #

4 C-3. A paricle moing wih a consan acceleraion from A o B in he sraigh line AB has elociies u and a A and B respeciely. If C is he mid-poin of AB hen he elociy of paricle while passing C will be + u (B) + u (C) - u (D) æ1 1ö ç + u è ø C-4. C-5. C-6. C-7. C-8. C-9. C-10. A sone A is dropped from res from a heigh h aboe he ground. A second sone B is simulaneously hrown erically up from a poin on he ground wih elociy. The line of moion of boh he sones is same. The alue of which would enable he sone B o mee he sone A midway (a mid poin) beween heir iniial posiions is gh (B) gh (C) gh (D) gh. A ball hrown up in acuum reurns afer 1 sec. Is posiion afer fie seconds will be same as afer : 7 sec (B) 3 sec (C) 4 sec (D) 3.5 sec The poins A, B, C and D lie in a erical line such ha AB = BC = CD. If a body falls from res a A, hen he imes of descen hrough AB, BC and CD are in he raio of 1 : : 3 (B) : 3 : 1 (C) 3 : 1 : (D)1: ( -1):( 3- ) A body when projeced erically up coers a oal disance D. The ime of is fligh is. If here were no graiy, he disance coered by i during he same ime is equal o 0 (B) D (C) D (D) 4D A paricle is projeced erically upwards from a poin A on he ground. I akes 1 ime o reach a poin B bu i sill coninues o moe up. If i akes furher ime o reach he ground from poin B hen heigh of poin B from he ground is 1 g( 1 + ) (B) g 1 (C) 1 g( 8 1 ) + (D) 1 g 1 Balls are hrown erically upward in such a way ha he nex ball is hrown when he preious one is a he maximum heigh. If he maximum heigh is 5m, he number of balls hrown per minue will be 40 (B) 50 (C) 60 (D) 10 An objec is ossed erically ino he air wih an iniial elociy of 8 m/s. Using he sign conenion upwards as posiie, how does he erical componen of he acceleraion a y of he objec (afer leaing he hand) ary during he fligh of he objec? On he way up a y > 0, on he way down a y > 0 (B) On he way up a y < 0, on he way down a y > 0 (C) On he way up a y > 0, on he way down a y < 0 (D) On he way up a y < 0, on he way down a y < 0 Secion : (D) Graph relaed quesions D-1*. Which of he following - graphs are no possible : (B) (C) (D) A-479 Indra Vihar, Koa Rajashan Page No. # 3

5 D-. The figure shows a elociy-ime graph of a paricle moing along a sraigh line, 1 (ms ) (s) 0 The correc displacemen-ime graph of he paricle is shown as : x (m) x (m) (s) (B) (s) x (m) x (m) (C) (s) (D) (s) D-3. Figure shows he posiion ime graph of a paricle moing on he X-axis. D-4. D-5. he paricle is coninuously going in posiie x direcion (B) area under x cure shows he displacemen of paricle (C) he elociy increases up o a ime o, and hen becomes consan. (D) he paricle moes a a consan elociy up o a ime o, and hen sops. x The displacemen ime graph of a moing paricle is shown. The insananeous elociy of he paricle is negaie a he poin : C (C) E (B) D (D) F The ariaion of elociy of a paricle moing along a sraigh line is shown in he figure. The disance raelled by he paricle in 4 s is : C D E F 5 m (B) 30 m (C) 55 m (D) 60 m A-479 Indra Vihar, Koa Rajashan Page No. # 4

6 D-6. A paricle sars from res and moes along a sraigh line wih consan acceleraion. The ariaion of elociy wih displacemen S is : (B) (C) (D) S S S S D-7*. The acceleraion ime plo for a paricle (saring from res) moing on a sraigh line is shown in figure for gien ime ineral. The paricle has zero aerage acceleraion (B) The paricle has neer urned around. (C) The paricle has zero displacemen (D) The aerage speed in he ineral 0 o 10s is he same as he aerage speed in he ineral 10s o 0s. D-8. Which of he following graph correcly represens elociy-ime relaionship for a paricle released from res o fall freely under graiy? (B) (C) (D) D-9. If posiion ime graph of a paricle is sine cure as shown, wha will be is elociy-ime graph. (B) (C) (D) D-10. D-11. A man moes in x-y plane along he pah shown. A wha poin is his aerage elociy ecor in he same direcion as his insananeous elociy ecor. The man sars from poin P. A (B) B (C) C (D) D Posiion-ime graph is shown which is a semicircle from = o = 8 sec. Find ime a which he insananeous elociy, is equal o aerage elociy oer firs seconds 4.8 sec (B) 3. sec (C).4 sec (D) 5 sec A-479 Indra Vihar, Koa Rajashan Page No. # 5

7 Secion : (E) Variable Acceleraion E-1. For moion of an objec along he x-axis, he elociy depends on he displacemen x as = 3x x, hen wha is he acceleraion a x = m. 48 ms (B) 80 ms (C) 18 ms (D) 10 ms E-. The iniial elociy of a paricle is gien by u (a = 0) and he acceleraion by f, where f = a (here is ime and a is consan). Which of he following relaion is alid? = u + a (B) = u + a (C) = u + a (D) = u E-3. A paricle moes along a sraigh line according o he law S = a + b + c. The acceleraion of he paricle aries as : 3 S - (B) / 3 S (C) S (D) 5/ S. E-4. A poin moes recilinearly wih deceleraion whose modulus depends on he elociy of he paricle as a =- k where k is a consan, k > 0. A he iniial momen he elociy of paricle is 0. A some momen elociy of paricle is zero. find he disance raelled by he paricle ill ha insan. 0 = k (B) 0 = k (C) 0 = k (D) 3 0 = k E-5. An objec is moing along he x axis wih posiion as a funcion of ime gien by x = x(). Poin O is a x = 0. The objec is definiely moing oward O when dx/d < 0 (B) dx/d > 0 (C) d(x ) / d < 0 (D) d(x )/d > 0 E-6. A paricle sars moing recilinearly a ime = 0 such ha is elociy '' changes wih ime '' according o he equaion = where is in seconds and is in m/s. The ime ineral for which he paricle reards is < 1/ (B) 1/ < < 1 (C) > 1 (D) < 1/ and > 1 PART - II : MISCELLANEOUS QUESTIONS Comprehension Type Quesions Comprehension # 1 A paricle saring from res has a consan acceleraion of 4 m/s for 4 seconds. I hen reards uniformly for nex 8 seconds and comes o res. 1. Aerage acceleraion during he moion of he paricle is 4 m/s (B) zero (C) 8 m/s (D) 4 m/s. Aerage speed during he moion of he paricle is 8 m/s (B) zero (C) 4 m/s (D) 16 m/s 3. Aerage elociy during he moion of he paricle is zero (B) 8 m/s (C) m/s (D) 4 m/s A-479 Indra Vihar, Koa Rajashan Page No. # 6

8 Comprehension # The figure shows a elociy-ime graph of a paricle moing along a sraigh line 4. Choose he incorrec saemen. The paricle comes o res a = 0 s (B) = 5 s (C) = 8 s (D) none of hese 5. Idenify he region in which he rae of change of elociy D r of he paricle is maximum D 0 o s (B) o 4s (C) 4 o 6 s (D) 6 o 8 s 6. If he paricle sars from he posiion x 0 = 15 m, hen is posiion a = s will be 5 m (B) 5 m (C) 10 m (D) 15 m 7. The maximum displacemen of he paricle is 33.3 m (B) 3.3 m (C) 18.3 m (D) zero 8. The oal disance raelled by he paricle is 66.7 m (B) 51.6 m (C) zero (D) 36.6 m Comprehension # 3 The x- graph of a paricle moing along a sraigh line is shown in figure 9. The - graph of he paricle is correcly shown by (B) (C) (D) 10. The a- graph of he paricle is correcly shown by (B) (C) (D) 11. The speed-ime graph of he paricle is correcly shown by (B) (C) (D) A-479 Indra Vihar, Koa Rajashan Page No. # 7

9 Mach he Column : 1. In he s- equaion (s = ) mach he following : Table-1 Disance raelled in 3s (B) Displacemen in 1s (C) Iniial acceleraion (D) Velociy a 4s Table- (p) 0 uni (q) 15 uni (r) 5 uni (s) 10 uni 13. Column I gies some graphs for a paricle moing along x-axis in posiie x direcion. The ariables, x and represen speed of paricle, x coordinae of paricle and ime respeciely. Column II gies cerain resuling inerpreaion. Mach he graphs in Column I wih he saemens in Column II. Column I Column II - x graph x (p) Acceleraion of paricle is uniform (B) (q) Acceleraion of paricle is nonuniform - x graph x (C) - graph (r) Acceleraion of paricle is direcly proporional o (D) - graph (s) Acceleraion of paricle is direcly proporional o x. A-479 Indra Vihar, Koa Rajashan Page No. # 8

10 Asserion & Reason ype quesions 14. Saemen-1 : Posiie acceleraion in recilinear moion of a body does no imply ha he body is speeding up. Saemen- : Boh he acceleraion and elociy are ecors. Saemen-1 is rue, saemen- is rue and saemen- is correc explanaion for saemen-1. (B) Saemen-1 is rue, saemen- is rue and saemen- is NOT he correc explanaion for saemen-1. (C) Saemen-1 is rue, saemen- is false. (D) Saemen-1 is false, saemen- is rue. 15. Saemen -1 : A paricle haing zero acceleraion mus hae consan speed. Saemen - : A paricle haing consan speed mus hae zero acceleraion. Saemen-1 is rue, saemen- is rue and saemen- is correc explanaion for saemen-1. (B) Saemen-1 is rue, saemen- is rue and saemen- is NOT he correc explanaion for saemen-1. (C) Saemen-1 is false, saemen- is rue. (D) Saemen-1 is rue, saemen- is false. 16. Saemen-1 : A suden performed an experimen by moing a cerain block in a sraigh line. The elociy posiion graph canno be as shown. Saemen- : When a paricle is a is maximum posiion in recilinear moion is elociy mus be zero. x Saemen-1 is rue, saemen- is rue and saemen- is correc explanaion for saemen-1. (B) Saemen-1 is rue, saemen- is rue and saemen- is NOT he correc explanaion for saemen-1. (C) Saemen-1 is rue, saemen- is false. (D) Saemen-1 is false, saemen- is rue. 17. Saemen-1 : If he elociy ime graph of a body moing in a sraigh line is as shown here, he acceleraion of he body mus be consan. Saemen- : The rae of change of quaniy which is consan is always zero. Saemen-1 is rue, saemen- is rue and saemen- is correc explanaion for saemen-1. (B) Saemen-1 is rue, saemen- is rue and saemen- is NOT he correc explanaion for saemen-1. (C) Saemen-1 is false, saemen- is rue. (D) Saemen-1 is rue, saemen- is false. Single Correc Answer Type PART - I : MIXED OBJECTIVE 1. An objec moing wih uniform acceleraion has a elociy of 1.0 cm/s in he posiie x direcion when is x coordinae is 3.00 cm. If is x coordinae.00 s laer is 5.00 cm, wha is is acceleraion(in cm/s )? 16 (B) 16 (C) 1 (D) 8. A body sars from res and is uniformly accleraed for 30 s. The disance raelled in he firs 10 s is x 1, nex 10 s is x and he las 10 s is x 3. Then x 1 : x : x 3 is he same as 1 : : 4 (B) 1 : : 5 (C) 1 : 3 : 5 (D) 1 : 3 : 9 3. The posiion coordinae of a paricle ha is confined o moe along a sraigh line is gien by x = where x is measured from a conenien origin and is in seconds. Deermine he disance raelled by he paricle during he ineral from =1 sec o = 4 sec. 7m (B) 74m (C) 68m (D) 37m A-479 Indra Vihar, Koa Rajashan Page No. # 9

11 4. The deceleraion experienced by a moing moor boa, afer is engine is cu-off is gien by d 3 k d =-, where k is consan. If 0 is he magniude of he elociy a cu-off he magniude of he elociy a a ime afer he cu-off is : 0 / (B) (C) 0 e k (D) 0 0 k A lif is descending wih uniform acceleraion. To measure he acceleraion, a person in he lif drops a coin a he momen when lif was descending wih speed 6 f/s. The coin is 5 f aboe he floor of he lif a ime i is dropped. The person obseres ha he coin srikes he floor in 1 second. Calculae from hese daa, he acceleraion of he lif. [Take g = 3 f/s ] 0 f/s (B) 11 f/s (C) f/s (D) 1 f/s 6. A body sars wih an iniial elociy of 10 m/s and moes along a sraigh line wih a consan acceleraion. When he elociy of he paricle is 50 m/s he acceleraion is reersed in direcion. Find he elociy of he paricle when i reaches he saring poin. 70 m/s (B) 50 m/s (C) 45 m/s (D) 49 m/s 7. The displacemen of a paricle in a sraigh line moion is gien by s = The correc represenaion of he moion is s s s s (B) (C) (D). 8. A ball is hrown upwards wih speed from he op of a ower and i reaches he ground wih speed 3. Wha is he heigh of he ower? g (B) g 9. A sone falls freely from res and he oal disance coered by i in he las second of is moion equals he disance coered by i in he firs hree seconds of is moion. The sone remains in he air for 5 s (B) 8 s (C) 10 s (D) 15 s 10. The greaes acceleraion or deceleraion ha a rain may hae is a. The minimum ime in which he rain may reach from one saion o he oher separaed by a disance d is d a (B) d a (C) 4 g (C) 1 d a (D) 8 g (D) 11. Acceleraion ersus elociy graph of a paricle moing in a sraigh line saring from res is as shown in figure. The corresponding elociy-ime graph would be d a (B) (C) (D) 1. I akes one minue for a passenger sanding on an escalaor o reach he op. If he escalaor does no moe i akes him 3 minue o walk up. How long will i ake for he passenger o arrie a he op if he walks up he moing escalaor? 30 sec (B) 45 sec (C) 40 sec (D) 35 sec A-479 Indra Vihar, Koa Rajashan Page No. # 10

12 Muliple Correc Answer(s) Type 13. A paricle moes wih consan speed along a regular hexagon ABCDEF in he same order. Then he magniude of he aerage elociy for is moion from A o : F is /5 (B) D is /3 (C) C is 3 (D) B is 14. Mark he correc saemens for a paricle going on a sraigh line : if he elociy is zero a any insan, he acceleraion should also be zero a ha insan (B) if he elociy is zero for a ime ineral, he acceleraion is zero a any insan wihin he ime ineral (C) if he elociy and acceleraion hae opposie sign, he objec is slowing down (D) if he posiion and elociy hae opposie sign, he paricle is moing owards he origin 15. Le and a denoe he elociy and acceleraion respeciely of a body in one dimensional moion I I mus decrease when a < 0 (B) Speed mus increase when a > 0 (C) Speed will increase when boh and a are < 0 (D) Speed will decrease when <0 and a > Le and a denoe he elociy and acceleraion respeciely of a body : a can be non zero when = 0 (B) a mus be zero when = 0 (C) a may be zero when ¹ 0 (D) he direcion of a mus hae some correlaion wih he direcion of 17. A paricle iniially a res is subjeced o wo forces. One is consan, he oher is a rearding force proporional o he paricle elociy. In he subsequen moion of he paricle : he acceleraion will increase from zero o a consan alue (B) he acceleraion will decrease from is iniial alue o zero (C) he elociy will increase from zero o maximum and hen decrease (D) he elociy will increase from zero o a consan alue. 18. Pick he correc saemens : wo sones are dropped from he same poin afer an ineral of 1 second. If g is 10 ms, hen he separaion afer 3 seconds of he release of firs sone is 5m (B) a ball projeced up wih a elociy reaches a poin P in is pah a 1 and seconds. The heigh of poin P aboe he ground is 1 g 1 (C) a ball projeced up wih elociy reaches a poin P in is pahs a 1 and seconds. Then = 1 g ( 1 + ) (D) he acceleraion of a body hrown erically upwards is g a he highes poin 19. Saring from res a paricle is firs acceleraed for ime 1 wih consan acceleraion a 1 and hen sops in ime wih consan reardaion a. Le 1 be he aerage elociy in his case and s 1 he oal displacemen. In he second case, i is acceleraed for he same ime 1 wih consan acceleraion a 1 and comes o res wih consan reardaion a in ime 3. If is he aerage elociy in his case and s he oal displacemen, hen : = 1 (B) 1 < < 4 1 (C) s = s 1 (D) s 1 < s < 4s 1 A-479 Indra Vihar, Koa Rajashan Page No. # 11

13 0. A paricle is projeced erically upwards wih elociy u from a poin A, when i reurns o poin of projecion: Is aerage speed is u/ (B) Is aerage elociy is zero (C) Is displacemen is zero (D) Is aerage speed is u 1. A paricle moing wih a speed changes direcion by an angle q, wihou change in speed. The change in he magniude of is elociy is zero. (B) The change in he magniude of is elociy is sin(q/). (C) The magniude of he change in elociy is sin(q/) (D) The magniude of he change in is elociy is (1 cosq).. A paricle has iniial elociy 10 m/s. I moes due o consan rearding force along he line of elociy which produces a reardaion of 5 m/s. Then he maximum displacemen in he direcion of iniial elociy is 10 m (B) he disance raelled in firs 3 seconds is 7.5 m (C) he disance raelled in firs 3 seconds is 1.5 m (D) he disance raelled in firs 3 seconds is 17.5 m. 3. A bead is free o slide down a smooh wire ighly sreched beween poins A and B on a erical circle. If he bead sars from res a A, he highes poin on he circle : is elociy on arriing a B is proporional o cosq (B) is elociy on arriing a B is proporional o anq (C) ime o arrie a B is proporional o cosq (D) ime o arrie a B is independen of q 4. The figure shows he elociy () of a paricle ploed agains ime () The paricle changes is direcion of moion a some poin (B) The acceleraion of he paricle remains consan (C) The displacemen of he paricle is zero (D) The iniial and final speeds of he paricle are he same 5. Velociy-ime graph for a car is semicircle as shown here. Which of he following is correc : Car mus moe in circular pah. (B) Acceleraion of car is neer zero. (C) Mean speed of he paricle is p/4 m/s. (D) The car makes a urn once during is moion. A-479 Indra Vihar, Koa Rajashan Page No. # 1

14 PART - II : SUBJECTIVE QUESTIONS 1. A paricle coers each 3 1 of he oal disance wih speed 1, and 3 respeciely. Find he aerage speed of he paricle?. A paricle moes along a semi circular pah A o B in a ime T as shown in he following fig. (a) Deermine he aerage speed of he paricle. (b) Deermine he aerage elociy of he paricle. 3. An engine drier running a rain a full speed suddenly applies brakes and shus off seam. The rain hen raels 4 m in he firs second and m in he nex second. Assuming ha he brakes produce a consan reardaion, find (a) original speed of he rain, (b) he ime elapsed before i comes o res (c) he disance raelled during he ineral. (d) If he lengh of he rain is 44 m, find he ime ha he rain akes o pass an obserer sanding a a disance 100 m ahead of he rain a he ime when he brake was applied. 4. A paricle moing along a sraigh line wih consan acceleraion is haing iniial and final elociy as 5 m/s and 15 m/s respeciely in a ime ineral of 5 s. Find he disance raelled by he paricle and he acceleraion of he paricle. If he paricle coninues wih same acceleraion, find he disance coered by he paricle in he 8h second of is moion. 5. A bird flies wih a speed = m/s along a sraigh line, where is ime in seconds. The disance (in mere) raelled by he bird during firs four seconds is equal o? 6. A car moing along a sraigh line sars from res wih uniform acceleraion a = m/s, hen moes wih consan elociy and finally comes o res deceleraing a he same rae. The oal ime of moion is 10 s and aerage speed during complee moion is 3. m/s. How long (in sec) did he car moe uniformly? 7. From he op of a ower, a sone is hrown up. I reaches he ground in 5 s. A second sone is hrown down wih he same speed and reaches he ground in 1 s. A hird sone is released from res and reaches he ground in X sec. Find X. 8. A a disance L = 400m from he raffic ligh brakes are applied o a locomoie moing a a elociy = 54 km/hr. Deermine he posiion of he locomoie relaie o he raffic ligh 1 minue afer he applicaion of he brakes if is acceleraion is 0.3m/sec. 9. A paricle goes from A o B wih a speed of 40km/h and B o C wih a speed of 60km/h. If AB = 6BC, he aerage speed in km/h beween A and C is [Hin: Aerage speed = oal disance raelled ime aken 10. An objec moing wih uniform acceleraion has a elociy of 1.0 cm/s in he posiie x direcion when is x coordinae is 3.00 cm. If is x coordinae.00 s laer is 5.00 cm, wha is is acceleraion? ] A-479 Indra Vihar, Koa Rajashan Page No. # 13

15 11. A paricle is moing along x-axis. Iniially i is locaed 5 m lef of origin and i is moing away from he origin and slowing down. In his coordinae sysem, wha are he signs of he iniial elociy and acceleraion. 0 a 1. The elociy-ime graph of he paricle moing along a sraigh line is shown. The rae of acceleraion and deceleraion is consan and i is equal o 5 ms. If he aerage elociy during he moion is 0 ms 1, hen find he alue of. 13. The figure shows he graph of a paricle moing in sraigh line. Find he ime when paricle reurns o he saring poin. 14. A sone is dropped from a heigh h. Simulaneously anoher sone is hrown up from he ground wih such a elociy ha i can reach a heigh of 4h. Find he ime when wo sones cross each oher. 15. A balloon is ascending erically wih an acceleraion of 0.m/s. Two sones are dropped from i a an ineral of sec. Find he disance beween hem 1.5 sec afer he second sone is released. (use g = 9.8m/s ) 16. A speeder in an auomobile passes a saionary policeman who is hiding behind a bill board wih a moorcycle. Afer a.0 sec delay (reacion ime) he policeman acceleraes o his maximum speed of 150 km/hr in 1 sec and caches he speeder 1.5 km beyond he billboard. Find he speed of speeder in km/hr. 17. The posiion coordinae of a paricle ha is confined o moe along a sraigh line is gien by x = where x is measured from a conenien origin and is in seconds. Deermine he disance raelled by he paricle during he ineral from =1 sec o = 4 sec. A-479 Indra Vihar, Koa Rajashan Page No. # 14

16 PART - I : IIT-JEE PROBLEMS (PREVIOUS YEARS) * Marked Quesions are haing more han one correc opion. 1. A ball is dropped erically from a heigh d aboe he ground. I his he ground and bounces up erically o a heigh d/. Neglecing subsequen moion and air resisance, is elociy aries wih he heigh h aboe he ground as [JEE '000, 1/35] (B) (C) (D). A block is moing down a smooh inclined plane saring from res a ime = 0. Le S n be he disance raelled by he block in he ineral = n 1 o = n. The raio Sn Sn+ 1 is [JEE (Scr.), 004, 3] n - 1 n (B) n -1 n + 1 (C) n + 1 n -1 (D) n n A paricle is iniially a res, I is subjeced o a linear acceleraion a, as shown in he figure. The maximum speed aained by he paricle is [JEE Scr. 004; 3] 605 m/s (B) 110 m/s (C) 55 m/s (D) 550 m/s 4. The elociy displacemen graph of a paricle moing along a sraigh line is shown. The mos suiable acceleraion-displacemen graph will be [JEE Scr. 005; 3] (B) (C) (D) A-479 Indra Vihar, Koa Rajashan Page No. # 15

17 PART - II : AIEEE PROBLEMS (PREVIOUS YEARS) 1. If a body loses half of is elociy on peneraing 3 cm in a wooden block, hen how much will i penerae more before coming o res? [AIEEE - 00, 4/300] (1) 1 cm () cm (3) 3 cm (4) 4 cm. From a building wo balls A and B are hrown such ha A is hrown upwards and B downwards (boh erically). If V A and V B are heir respecie elociies on reaching he ground, hen [AIEEE - 00, 4/300] (1) B > A () A = B (3) A > B (4) heir elociies depends on heir masses 3. Speeds of wo idenical cars are u and 4u a a specific insan. The raio of he respecie disances a which he wo cars are sopped from ha insan is : [AIEEE - 00, 4/300] (1) 1 : 1 () 1 : 4 (3) 1 : 8 (4) 1 : The coordinaes of a moing paricle a any ime are gien by x = a 3 and y = b 3. The speed of he paricle a ime is gien by : [AIEEE - 003, 4/300] (1) a + b () 3 a + b (3) a + b (4) a + b 5. A car moing wih a speed of 50 km/hr, can be sopped by brakes afer a leas 6 m. if he same car is moing a a speed of 100 km/hr, he minimum sopping disance is : [AIEEE - 003, 4/300] (1) 1 m () 18 m (3) 4 m (4) 6 m 6. A ball is released from he op of a ower of heigh h meres. I akes T seconds o reach he ground. Wha is he posiion of he ball in T/3 seconds? [AIEEE - 004, 4/300] (1) h/9 mere from he ground () 7h/9 mere from he ground (3) 8h/9 mere from he ground (4) 17h/9 mere from he ground 7. An auomobile raelling wih a speed of 60 km/h, can brake o sop wihin a disance of 0 m. If he car is going wice as fas, ie. 10 km/h, he sopping disance will be [AIEEE - 004, 4/300] (1) 0 m () 40 m (3) 60 m (4) 80 m 8. The relaion beween ime and disance x is = ax + bx, where a and b are consans. The acceleraion is: [AIEEE 005, 4.300] (1) ab () b (3) a 3 (4) a 3 9. A car, saring from res, acceleraes a he rae f hrough a disance S, hen coninues a consan speed for ime and hen deceleraes a he rae f o come o res. If he oal disance raelled is 15 S, hen : [AIEEE 005, 4/300] (1) S = f () S = f (3) S = f (4) S = f A paricle is moing easwards wih a elociy of 5 ms 1. In 10 second he elociy changes o 5 ms 1 norhwards. The aerage acceleraion in his ime is : [AIEEE 005, 4/300] (1) 1 ms 1 owards norh-wes () 1 ms owards norh (3) zero (4) 1 ms owards norh-wes. A-479 Indra Vihar, Koa Rajashan Page No. # 16

18 11. A parachuis afer bailing ou falls 50 m wihou fricion. When parachue opens, i deceleraes a m/s. He reaches he ground wih a speed of 3 m/s. A wha heigh, did he bail ou? [AIEEE 005, 4/300] (1) 91 m () 18 m (3) 93 m (4) 111 m 1. A paricle locaed a x = 0 a ime = 0, sars moing along he posiie x-direcion wih a elociy ha aries as = a x The displacemen of he paricle aries wih ime as [AIEEE-006, 3/180] (1) 1/ () 3 (3) (4) 13. The elociy of a paricle is = 0 + g + f. If is posiion is x = 0 a = 0, hen is displacemen afer uni ime ( = 1) is [AIEEE 007, 3/10] (1) 0 + g + 3f () 0 + g + 3 f (3) 0 + g + f (4) 0 + g + f 14. A paricle has an iniial elociy of 3 î + 4ĵ and an acceleraion of 0.4î + 0.3ĵ. Is speed afer 10 s is : (1) 7 unis () 7 unis (3) 8.5 unis (4) 10 unis [AIEEE 009, 4/144] r 15. A paricle is moing wih elociy = K(y î + x ĵ), where K is a consan. The general equaion for is pah is: [AIEEE 010, 4/144] (1) y = x + consan () y = x + consan (3) xy = consan (4) y = x + consan d 16. An objec, moing wih a speed of 6.5 m/s, is deceleraed a a rae gien by =.5 d insananeous speed. The ime aken by he objec, o come o res, would be : [AIEEE 011] (1) 1s () s (3) 4s (4) 8s where is he NCERT QUESTIONS 1. In which of he following examples of moion, can he body be considered approximaely a poin objec : (a) a railway carriage moing wihou, jerks beween wo saions (b) a monkey siing on op of a man cycling smoohly on a circular rack. (c) a spinning cricke ball ha urns sharply on hiing he ground. (d) a umbling beaker ha has slipped off he edge of a able.. The posiion-ime (x-) graphs for wo children?a and B reurning from heir school O o heir homes P and Q respeciely are shown in figure. Choose he correc enries in he brackes below : (a) (A/B) lies closer o he school han (B/A) (b) (A/B) sars from he school earlier han (B/A) (c) (A/B) walks faser han (B/A) (d) A and B reach home a he (same/differen) ime (e) (A/B) oerakes (B/A) on he road (once/wice) 3. A woman sars from her home a 9.00 am, walks wih a speed of 5 km h 1 on a sraigh road up o her office.5 km away, says a he office up o 5.00 pm, and reurns home by an auo wih a speed of 5 km h 1. Choose suiable scales and plo he x- graph of her moion. A-479 Indra Vihar, Koa Rajashan Page No. # 17

19 4. A drunkard walking in a narrow lane akes 5 seps forward and 3 seps backward, followed again by 5 seps forward and 3 seps backward, and so on. Each sep is 1 m long and requires 1 s. Plo he x- graph of his moion. Deermine graphically and oherwise how long he drunkard akes o fall in a pi 13 m away from he sar. 5. A car moing along a sraigh highway wih speed of 16 km h 1 is brough o a sop wihin a disance of 00 m. Wha is he reardaion of he car (assumed uniform), and how long does i ake for he car o sop? 6. A player hrows a ball upwards wih an iniial speed of 9.4 m s 1. (a) Wha is he direcion of acceleraion during he upward moion of he ball? (b) Wha are he elociy and acceleraion of he ball a he highes poin of is moion? (c) Choose he x = 0 m and = 0 s o be he locaion and ime of he ball a is highes poin, erically downward direcion o be he posiie direcion of x-axis and gie he signs of posiion, elociy and acceleraion of he ball during Is upward, and downward moion. (d) To wha heigh does he ball rise and aler how long does he ball reurn o he player's hands? (Take 9 = 9.8 m s and neglec air resisance). 7. A ball is dropped from a heigh of 90 m on a floor. A each collision wih he floor, he ball loses one enh of is speed, Plo he speed-ime graph of is moion beween = 0 o 1 s. 8. A man walks on a sraigh road from his home o a marke.5 km away wih a speed of 5 km h 1 Finding he marke closed, he insanly urns and walks back home wih a speed of 7.5 km h 1. Wha is he : (a) magniude of aerage elociy, and (b) aerage speed of he man oer he ineral of ime (i) 0 o 30 min. (ii) 0 o 50 min (iii) 0 o 40 min? [Noe: You will appreciae from his exercise why i is beer o define aerage speed as oal pah lengh diided by ime, and no as magniude of aerage elociy. You would no like o ell he ired man on his reurn home ha his aerage speed was zero!] 9. Look a he graphs (a) o (d) (Fig.) carefully and sae, wih reasons which of hese canno possibly represen one-dimensional moion of a paricle. (a) (b) (c) (d) 10. Figure shows he x- plo of one-dimensional moion of a paricle. Is i correc o say from he graph ha he paricle moes in a sraigh line for < 0 and on a parabolic pah for >0? If no, sugges a suiable physical conex for his graph. A-479 Indra Vihar, Koa Rajashan Page No. # 18

20 11. Sugges a suiable physical siuaion for each of he following graphs (Fig) : (a) (b) (c) 1. Figure gies he x- plo of a paricle execuing one-dimensional simple harmonic moion. (You will learn abou his moion in more deail in Chaper14). Gie he signs of posiion, elociy and acceleraion ariables of he paricle a = 0.3 s, 1. s, 1. s. 13. Figure gies he x- plo of a paricle in one-dimensional moion. Three differen equal inerals of ime are shown. In which ineral is he aerage speed greaes, and in which is i he leas? Gie he sign of aerage elociy for each ineral. 14. Figure gies a speed-ime graph of a paricle in moion along a consan direcion. Three equal inerals of ime are shown. In which ineral is he aerage acceleraion greaes in magniude? In which ineral is he aerage speed greaes? Choosing he posiie direcion as he consan direcion of moion, gie he signs of and a in he hree inerals. Wha are he acceleraions a he poins A, B. C and D? A-479 Indra Vihar, Koa Rajashan Page No. # 19

21 15. The speed-ime graph of a paricle moing along a fixed direcion is shown in figure. Obain he disance raersed by he paricle beween (a) = 0 s o 10 s, (b) = s o 6 s. 16. The elociy lime graph of a paricle in one-dimensional moion is shown in figure. Which of he following formulae are correc for describing he moion of he paricle oer he ime-ineral 1 o. (a) x( ) = x( 1 ) + ( 1 ) ( 1 ) + (1/) a ( 1 ) (b) ( ) = ( 1 ) + a ( 1 ) (c) aerage = (x( ) x( 1 )) / ( 1 1 ) (d) aerage = (( ) ( 1 )) / ( 1 ) (e) x( ) = x( 1 ) + aerage ( 1 ) + (1/) a aerage ( 1 ) (f) x( ) x( 1 ) = area under he - cure bounded by he -axis and he doed line shown. A-479 Indra Vihar, Koa Rajashan Page No. # 0

22 EXERCISE-1 PART - I A-1. (B) A-. B-1. (B) B-*. (AD) B-3.* (AC) B-4. C-1. C-. (D) C-3. C-4. (C) C-5. C-6. (D) C-7. (C) C-8. (D) C-9. (C) C-10. (D) D-1*. (BCD) D-. (C) D-3. (D) D-4. (C) D-5. (C) D-6. (B) D-7*. (ABD) D-8. D.9 (C) D.10 (C) D.11 (B) E-1. (B) E-. (B) E-3. E-4. E-5. (C) E-6. (B) PART - II 1. (B). 3. (B) 4. (B) 5. (C) (B) 10. (D) 11. (C) 1. r (B) q (C) s (D) p 13. q, s (B) p (C) p (D) q, r (D) (B) EXERCISE- PART - I 1.. (C) 3. (B) 4. (D) 5. (C) (D) 8. (C) (D) 11. (D) 1. (B) 13. (ACD) 14. (BCD) 15. (CD) 16. (AC) 17. (BD) 18. (ABCD) 19. (AD) 0. (ABC) 1. (AC). (AC) 3. (AD) 4. (ABCD) 5. (C) PART - II pr. (a) T (b) R T 3. (a) 5 m/s. (b) 1.5 sec. (c) m (d) 9 seconds 4. 50m ; m/s ; 0 m m 9. 4km/hr cm/s a ¾ + Because paricle is slowing down so elociy & acceleraion are in opposie direcion s sec m F HG I h m km/hr 8gKJ A-479 Indra Vihar, Koa Rajashan Page No. # 1

23 EXERCISE-3 PART - I 1.. (B) 3. (C) 4. (B) PART - II 1. (1). () 3. (4) 4. () 5. (3) 6. (3) 7. (4) 8. (3) 9. (3) 10. (1) 11. (3) 1. (3) 13. () 14. (1) 15. (4) 16. () 1. (a), (b) EXERCISE-4. (a) A...B, (b) A...B, (c) B...A, (d) Same, (e) B...A...once s ms ; 11.4 s 6. (a) Verically downwards ; (b) zero elociy, acceleraion of 9.8 m s downwards ; (c) x > 0 (upwards and downward moion); < 0 (upward), > 0 (downward), a > 0 hroughou ; (d) 44.1 m, 6s. 8. (a) 5 km h 1, 5 km h 1 ; (b) 0; 6 km h 1 ; (c) kmh, kmh All he four graphs are impossible. (a) a paricle canno hae wo differen posiions ae he same ime; (b) a paricle canno hae elociy in opposie direcions a he same ime ; (c) speed is always non-negaie; (d) oal pah lengh of a paricle can neer decreases wih ime. (Noe, he arrows on he graphs are meaningless). 10. No, wrong. x- plo does no show he rajecory of a paricle. Conex : A body is dropped from a ower (x = 0) a = (a) A ball a res on a smooh floor is kicked, i rebounds from a wall wih reduced speed and moes o he opposie wall which sops i; (b) A ball hrown up wih some iniial elociy rebounding from he floor wih reduced speed afer each hi; (c) A uniformly moing cricke ball urned back by hiing i wih a ba for a ery shor ime-ineral. 1. x < 0, < 0, a > 0; x > 0, > 0, a < 0; x < 0, > 0, a > Greaes in 3, leas in ; > 0 in 1 and, < 0 in Acceleraion magniude greaes in ; speed greaes in 3; > 0 in 1, and 3; a > 0 in 1 and 3, a < 0 in ; a = 0 a A, B, C, D. 15. (a) 60 m, 6 m s 1 ; (b) 36 m, 9 m s (c), (d), (f) A-479 Indra Vihar, Koa Rajashan Page No. #