Motion in a Straight Line

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2 Moion in Srigh Line. Preei reched he mero sion nd found h he esclor ws no working. She wlked up he sionry esclor in ime. On oher dys, if she remins sionry on he moing esclor, hen he esclor kes her up in ime. he ime ken by her o wlk up on he moing esclor will be: (7-Delhi). + b. c. d. +. he x nd y coordines of he pricle ny ime re x 5 nd y, respeciely, where x nd y re in meres nd in seconds. he ccelerion of he pricle s is: (7-Delhi). 5 m/s b. 4 m/s c. 8 m/s d.. A bll of mss kg is hrown ericlly upwrds nd reurns o he ground fer seconds. Anoher bll, hrown 6 wih ericl lso sys in ir for he sme ime before i ouches he ground. he rio of he wo heighs re: (7-Gujr). : b. : c. : d. : 4. A bulle of mss g moing horizonlly wih elociy of 4 ms srikes wooden block of mss kg which is suspended by ligh inexensible sring of lengh 5 m. As resul, he cener of griy of he block is found o rise ericl disnce of cm. he speed of he bulle fer i emerges ou horizonlly from he block will be: (6 - II). ms b. 6 ms c. ms d. 8 ms 5. wo crs P nd Q sr from poin he sme ime in srigh line nd heir posiions re represened by X P () + b nd X Q () f. A wh ime do he crs he he sme elociy? (6 - II). + f b ( + ) b. f b ( + ) c. f + b d. + f b ( ) 6. If he elociy of pricle is A + B, where A nd B re consns, hen he disnce relled by i beween s nd s is: (6 - I). A + 4B b. A + 7B c. A+ 7 B d. A + B 7. A pricle of uni mss undergoes one dimensionl moion such h is elociy ries ccording o (x) βx n where β nd n re consns nd x is he posiion of he pricle. he ccelerion of he pricle s funcion of x, is gien by: (5). nβ x 4n b. β x n + c. nβ e 4n + d. nβ x n 8. A sone flls freely under griy. I coers disnces h, h nd h in he firs 5 seconds, he nex 5 seconds nd he nex 5 seconds respeciely. he relion beween h, h nd h is: (). h h h b. h h h h h c. h d. h h nd h h 5 9. he moion of pricle long srigh line is described by equion : x where x is in mere nd in second. he rerdion of he pricle when is elociy becomes zero, is: ( Pre). 4 ms b. Zero c. 6 ms d. ms. A pricle coers hlf of is ol disnce wih speed nd he res hlf disnce wih speed. Is erge speed during he complee journey is: ( Mins). b. + + c. + d.

3 NEE Yers. A boy snding he op of ower of m heigh drops sone. Assuming g m/s, he elociy wih which i his he ground is: ( Pre).. m/s b.. m/s c. 4. m/s d. 5. m/s. A pricle hs iniil elociy i ˆ+ 4j ˆnd hs ccelerion.4i ˆ+.j ˆ. Is speed fer s is:. unis b. 7 unis ( Pre) c. 7 unis d. 8.5 unis. Six ecors, hrough f he he mgniudes nd direcions indiced in he figure. Which of he following semens is rue? ( Pre) 8. A pricle moes in srigh line wih consn ccelerion. I chnges is elociy from ms o ms while pssing hrough disnce 5 m in second. he lue of is (8). b. 9 c. d A pricle shows disnce-ime cure s gien in his figure. he mximum insnneous elociy of he pricle is round he poin (8). b+ e f c. d+ c f b c d e f b. b+ c f d. d+ e f 4. A pricle moes disnce x in ime ccording o equion x ( + 5). he ccelerion of pricle is proporionl o: ( Pre). (Velociy) / b. (Velociy) / c. (Disnce) d. (Disnce) - 5. A pricle srs is moion from res under he cion of consn force. If he disnce coered in firs seconds is S nd h coered in he firs seconds is S, hen: (9). S S b. S 4S c. S S d. S S 6. A bus is moing wih speed of ms - on srigh rod. A scooeris wishes o oerke he bus in s. If he bus is disnce of km from he scooeris, wih wh speed should he scooeris chse he bus? (9). 4 ms b. 5 ms c. ms d. ms 7. he disnce relled by pricle sring from res 4 nd moing wih n ccelerion ms, in he hird second is (8). m b. 9 m c. 6 m d. 4 m. D b. A c. B d. C. A pricle moing long x-xis hs ccelerion f, ime, gien by, f f where f nd re consns. he pricle hs zero elociy. In he ime inerl beween nd he insn when f, he pricle s elociy ( x ) is: (7). f b. f c. f d. f. A cr moes from X o Y wih uniform speed u nd reurns o Y wih uniform speed d. he erge speed for his round rip is: (7). u d b. d u d + u c. u + d du d. d + u. A pricle sring from he origin (, ) moes in srigh line in he (x, y) plne. Is coordines ler ime re (, ). he ph of he pricle mkes wih he x-xis n ngle of: (7). 45 b. 6 c. d.. he posiion x of pricle wih respec o ime long x-xis is gien by x 9 where x is in meres nd in second. Wh will be he posiion of his pricle when i chiees mximum speed long he +e x direcion? (7). 54 m b. 8 m c. 4 m d. m

4 Moion in Srigh Line 4. wo bodies, A (of mss kg) nd B (of mss kg) re dropped from heighs of 6 m nd 5 m, respeciely. he rio of he ime ken by hem o rech he ground is: (6). 5/4 b. 8/5 c. 5/8 d. 4/5 5. A cr runs consn speed on circulr rck of rdius m, king 6.8 s for eery circulr lp. he erge elociy nd erge speed for ech circulr lp respeciely is: (6)., b., m/s c. m/s, m/s d. m/s, 6. A pricle moes long srigh line OX. A ime (in seconds) he disnce x (in meers) of he pricle from O is gien by x 4 +. How long would he pricle rel before coming o res? (6). 4 m b. 8 m c. 56 m d. 4 m 7. he ecors A nd B re such h A+ B A B. he ngle beween he wo ecors is (6). 45 b. 9 c. 6 d A bll is hrown ericlly upwrd. I hs speed of m/s when i hs reched one hlf of is mximum heigh. How high does he bll rise? (king g m/s ) (5). 6 m b. m c. 4 m d. 8 m 9. wo boys re snding he ends A nd B of ground, where AB. he boy B srs running in direcion perpendiculr o AB wih elociy. he boy A srs running simulneously wih elociy nd cches he oher boy in ime, where is: (5). b. + ( ) ( ) c. /( ) d. /( + ). he displcemen x of pricle ries wih ime s x e -α + be β, where, b, α nd β re posiie consns. he elociy of he pricle will (5). Be independen of β b. Drop o zero when α β c. Go on decresing wih ime d. Go on incresing wih ime. A sone ied o he end of sring of m long is whirled in horizonl circle wih consn speed. If he sone mkes reoluions in 44 seconds, wh is he mgniude nd direcion of ccelerion of he sone? (5). π ms - nd direcion long he rdius owrds he cenre b. π ms - nd direcion long he rdius wy from he cenre c. π ms - nd direcion long he ngen o he circle d. π ms - nd direcion long he rdius owrds he cenre. If ecor i ˆ+ j ˆ+ 8kˆ is perpendiculr o he ecor 4j ˆ 4i ˆ+αkˆ hen he lue of α is (5). / b. / c. d.. If bll is hrown ericlly upwrds wih speed u, he disnce coered during he ls seconds of is scen is: (). u b. g c. u g d. (u + g) 4. A mn hrows bll wih he sme speed ericlly upwrds one fer he oher n inerl of seconds. Wh should be he speed of he hrow so h more hn wo blls re in he sky ny ime? (Gien g 9.8 m/s ) (). More hn 9.6 m/s b. A les 9.8 m/s c. Any speed less hn 9.6 m/s d. Only wih speed 9.6 m/s 5. A pricle is hrown ericlly upwrd. Is elociy hlf of he heigh is m/s, hen he mximum heigh ined by i: (g m/s ) (). 8 m b. m c. m d.6 m 6. he wih of rier is km. he elociy of bo is 5 km/hr. he bo coered he wih of rier wih shores will possible ph in 5 min. hen he elociy of rier srem is: (). km/hr b. 4 km/hr c. 9 km / hr d. 4 km / hr 7. Moion of pricle is gien by equion S ( ) m. he lue of ccelerion of he pricle sec. is: (). m/s b. m/s c. m/s d. 6 m/s

5 NEE Yers 8. For pricle displcemen ime relion is x +. Is displcemen when is elociy is zero: (999). m b. 4 m c. d. None of hese 9. A pricle srs from res wih consn ccelerion. he rio of erge elociy o he ime erge elociy is: (999). b. 4 c. 4 d. 4. he speed of bo is 5 km/hr is sill wer. I crosses rier of wih km long he shores possible ph in 5 minues. he elociy of rier wer is: (998). km/hr b. 4 km/hr c. 5 km/hr d. km/hr 4. he posiion x of pricle ries wih ime, () s x b. he ccelerion will be zero ime is equl o: (997). b. Zero b c. b d. b 4. If cr res cceleres uniformly o speed of 44 km/h in sec, i coers disnce of: (997). 44 cm b. 98 cm c. m d. 4 m 4. A body dropped from heigh) h wih iniil elociy zero, srikes he ground wih elociy m/s. Anoher body of sme mss dropped from he sme heigh h wih n iniil elociy of 4 m/s. he finl elociy of second mss, wih which i srikes he ground is: (996). 5 m/s b. m/s c. m/s d. 4 m/s 44. he ccelerion of pricle is incresing linerly wih ime s b. he pricle srs from origin wih n iniil elociy. he disnce relled by he pricle in ime will be: (995). + b b. + b c. + b d. + b he wer drop flls regulr inerls from p 5 m boe he ground. he hird drop is leing he p insn he firs drop ouches he ground. How fr boe he ground is he second drop h insn? (995)..75 m b. 4. m c..5 m d..5 m 46. A cr cceleres from res consn re α for some ime fer which i deceleres consn re β nd comes o res. If ol ime elpsed is, hen mximum elociy cquired by cr will be: (994). ( ) α β αβ c. ( α+β) αβ b. ( ) α +β αβ d. αβ α+β 47. A pricle moes long srigh line such h is displcemen ny ime is gien by s ( ) meres. he elociy when he ccelerion is zero is: (994). m/s b. 4 m/s c. 9 m/s d. 5 m/s 48. he elociy of rin increses uniformly from km/h o 6 km/h in 4 hours. he disnce relled by he rin during his period, is: (994). 6 km b. 8 km c. km d. km 49. he displcemen ime grph of moing pricle is shown below. he insnneous elociy of he pricle is negie he poin: (994) Displcemen C ime D. E b. F c. C d. D 5. A body srs from res, wh is he rio of he disnce relled by he during he 4 h nd rd second? (99). 7 5 b. 5 7 E c. 7 F d Which of he following cure does no represen moion in one dimension? (99). c. b. d.

6 Moion in Srigh Line 5. A body dropped from op of ower fll hrough 4 m during he ls wo seconds of is fll. he heigh of ower is (g m/s ): (99). 6 m b. 45 m c. 8 m d. 5 m 5. A cr moes disnce of m. I coers he firs hlf of he disnce speed 4 km/h nd he second hlf of disnce speed. he erge speed is 48 km/h. he lue of is: (99). 56 km/h b. 6 km/h c. 5 km/h d. 48 km/h 54. A bus relling he firs one-hird disnce speed of km/h, he nex one-hird km/h nd ls one-hird 6 km/h. he erge speed of he bus is: (997). 9 km/h b. 6 km/h c. 8 km/h d. 48 km/h 55. A cr coers he firs hlf of he disnce beween wo plces 4 km/h nd noher hlf 6 km/h. he erge speed of he cr is: (99). 4 km/h b. 48 km/h c. 5 km/h d. 6 km/h 56. Wh will be he rio of he disnce moed by freely flling body from res in 4h nd 5h seconds of journey? (989). 4 : 5 b. 7 : 9 c. 6 : 5 d. : 57. A cr is moing long srigh rod wih uniform ccelerion. If psses hrough wo poins P nd Q sepred by disnce wih elociy km/ h nd 4 km/h respeciely. he elociy of he cr midwy beween P nd Q is: (988).. km/h b. Km / h c. 5 Km / h d. 5 km/h

7 4 NEE Yers Answer Key b b c b c c d b b c d b b d b d c d b d b d b b b d b b c b c c d c d c b b b c b b c EXPLANAIONS. (b) NCER (XI) Ch -, Pg. 4 V Preei s elociy V Esclor s elociy disnce speed V + V + +. (b) NCER (XI) Ch -, Pg. 4 x 5 y dy 5 4 4m/s x 4ms y. (c) NCER (XI) Ch - 4, Pg. 78 V y sme for boh cses V H y g H H since ll re sme for boh cses 4. () NCER (XI) Ch - 4 AB 5 m Apply conserion of liner momenum mu + m + MV 4 + ν + V. + V 4...() MgH MV V V V ms Subsiuing he lue of V in eq. (), we ge ( ) ( 4- ) ms - 5. (b) NCER (XI) Ch -, Pg. 4 X p () + b X Q () f V p + b V Q f s V p V Qs + b f

8 Moion in Srigh Line f b ( + ) 6. (c) NCER (XI) Ch - 4, Pg. 47 A + B A + B x ( ) A + B A B A 7B x ( ) + ( ) + 7. () NCER (XI) Ch -, Pg. 45 βx n d n So, nβ d Now βx nβx 4n nβ x n n ( )( ) 8. (c) NCER (XI) Ch -, Pg AB h ( ) g 5 h 5 m ( 4 ) - h 75 m h BC g [ 5 ] h CD g é5 - ù êë úû h 65 m h : h : h 5 : 75 : 65 : : 5 h h h 5 9. (d) NCER (XI) Ch -, Pg s A s d 6 ms Rerdion ( ). (b) NCER (XI) Ch -, Pg. 4 ime ime wih speed wih speed ol disnce A. Speed ol ime ken s s + s s + + s s. (b) NCER (XI) Ch -, Pg. 48 u u gh gh gh m/s. (c) NCER (XI) Ch -, Pg. 76 u + i ˆ+ 4ˆj +.4i ˆ+.j ˆ ( ) ( )( ) 7i ˆ+ 7j ˆ so, speed 7 unis. (d) NCER (XI) Ch -, Pg. 67 e d f f d+ e 4. (b) NCER (XI) Ch -, Pg. 74 x ( ) Accelerion, d elociy + 5 ( ) ( ) / 5. (b) NCER (XI) Ch -, Pg. 5 Since here is consn force, ccelerion will be consn. Disnce coered in firs seconds 5

9 6 NEE Yers consn ( S ) ( ) A V Disnce coered in firs seconds When f,f ( S ) ( ) S 4S And elociy Vx 6. (d) NCER (XI) Ch -, Pg. 5 Scooeris Bus km m Speed of bus ms Scooeris hs o coer km more disnce wih respec o disnce coered by bus, in s Le he speed of scooeris be x ms hen, disnce coered by scooeris m + disnce coered by bus x + x x ms Hence, he speed of scooeris is ms 7. () NCER (XI) Ch -, Pg. 48 Disnce relled in he rd second Disnce relled in s disnce relled in s. As, u rd S( s) rd 4 Gien ms S ( s) 5 m 8. (b) NCER (XI) Ch -, Pg. 48 u s Gien ms, u ms, s 5 m 4 ms ν u ν u + 9 s 9 9. (d) NCER (XI) Ch -, Pg. 4 ds Becuse he slope is highes C, ν is mximum.. (c) NCER (XI) Ch -, Pg. 45 Gien Accelerion ( f) f f consn d f d f o o d f V f o f f o f o f f f. (d) NCER (XI) Ch -, Pg. 4 ol disnce d + d d xy V yx u d V d d+ d Aerge speed d d + V V d u VuVd V + V. (b) NCER (XI) Ch -, u O, Le he pricle moing in srigh line mkes n ngle θ wih x-xis. d

10 > Moion in Srigh Line y slope n θ x Since, n θ, θ 6. () NCER (XI) Ch -, Pg. 48 Gien: x 9 - when, i chiees mximum speed long he +x direcion, he ccelerion will become zero. x 9 - d ( 9 ) 8 d d Now, ( 8 ) 8 6 Since, will be zero, 8-6 s Posiion of pricle (x) 9 () - () 4. (d) If body is dropped from heigh h, ime ken o h nd i is independen of g rech he ground mss. h h h (b) Aerge elociy For ech circulr lp 6.8 Aerge speed ol displcemen ime ken Disnce coer ed in circulr lp ke ken Disnce π r.4 68 m 68 m / s 6.8 x 6. (d) X disnce from O, ime X 4 + Velociy d( 4 + ) ( ) m / s When pricle will come o res, i.e. s Disnce relled by pricle before coming o res, Disnce 4 + () m Dis. 4 + () 4 m 7. (b) Le θ be ngle beween A nd B A+ B A B hen A+ B A B or ( A+ B ).( A+ B) ( A B)( A B) or A.A + A.B+ B.A + B.B A.A A.B B.A + B.B 8. (b) or 4ABcosθ or cosθ or θ 9 H H V V m/s u + gh H + g gh H m ( g m/s ) 9. (b) V > A B Since, he boy A hs o coer disnce long A o B nd componen of elociy long AB V 7 O ime X ( )

11 8 NEE Yers So, ime ken. (d) x e α + be β u ime of fligh 4 u g g u 9.6 m/s ( g 9.8 m/s ) αe -α + bβe β u mn α e α + bβe β As increses e α decreses nd increses. So increses wih ime. 5. (c) h ms -. () Frequency Number of reoluion in sec f 44 s- ω r f 4π f r 4p 4 π ms. (b) i ˆ+ j ˆ+ 8k,b ˆ 4i ˆ+ 4j ˆ+αkˆ Do Produciszero. If b ( i ˆ+ j ˆ+ 8kˆ)( 4i ˆ+ 4j ˆ+α kˆ) or, α 4 + 8α α / u. (b) Le ime of fligh be, hen g Le h be he disnce coered during ls second Velociy poin B B u g( ) C B h u u g g g u A h g g g H h B g 4. () In his cse ime of fligh of bll 4 sec. 6. () h/ h u g () h h m d u 4 (5) km/hr 6 5 ds d 7. (b) ( ) d A, sec m/s 8. (c) x + x ( ) ( ), x ( ) 9. (c) < > ime ds ds < > spce ds ds

12 Moion in Srigh Line (c) Accelerion b, i.e., d x b Inegring, + C b spce / 4 / ime Iniilly,, / herefore, b + 4. () km ' V r V mr V V mr r b Inegring gin, x + + C 6 When, x C. i.e., disnce relled by he pricle in ime V mr 5 km/hr 5 min d 5 V V 6 5 V mr r r 4 5 V V 5 6 V 9 V r km/hr 4. () Disnce (x) b r r r herefore elociy d () ( b ) b d d b b ( ) 6 or. 6b b 4. (d) Iniil elociy u, Finl elociy 44 km/h 4 m/s nd ime sec. Using u + / m/s. Agin, s u + () 4 m. 4. () Iniil elociy of firs body (u ) ; Finl elociy ( ) m/s nd iniil elociy of second body (u ) 4 m/s. () Heigh ( h).46 m g 9.8 herefore elociy of he second body, u + gh (4) m/s. + b () Heigh of p 5 m. For he firs drop, 5 u + g 5 or or sec. I mens h he hird drop lees fer one second of he firs drop, or ech drop lees fer eery.5 sec. Disnce coered by he second drop in.5 sec (.5) g.5m herefore disnce of he second drop boe he ground m. 46. (d) Iniil elociy (u) ; Accelerion in he firs phse α; Declrion in he second phse β nd ol ime. When cr is ccelering hen, Finl elociy () u + α + α Or nd when cr is decelering, hen α finl elociy β or. β herefore ol ime () + + α β β+α αβ + or. α β αβ α + β 47. (c) Displcemen (s) meres. ds elociy ( ) +

13 NEE Yers d ccelerion ( ) 6. When, we ge seconds. herefore elociy when he ccelerion is zero () () ( ) + 9 m/s. 48. () Iniil elociy (u) km/h; Finl elociy () 6 km/h nd ime () 4 hours. Velociy () 6 u + + ( 4) 6 Or, km/h. 4 herefore disnce relled in 4 hours is s u + ( 4) + (4) 6 km. 49. () he elociy () ds. herefore, insnneous elociy poin E is negie. 5. () Disnce coered in n h second is gien by sn u+ (n ) Here, u s ( 4 ) 5 s4 7 s + ( ) s 5 5. (b) In one dimensionl moion, he body cn he ime one lue of elociy bu no wo lues of elociies. 5. (b) Le h be heigh of he ower nd is he ime ken by he body o rech he ground. Here, u, g 5 s4 7 s + ( ) s 5 Or h g...(i) Disnce coered in ls wo second is 4 ( ) g - g( - ) 4 g g (Here, u ) 5 5 ( ) 4 ( ) 8 ( ) 8 6 sec From Eq. (i), we ge h () or h 45 m. 5. (b) xy V g x + y 4 V V 6 km/h xyz 54. (c) Alier erge speed xy + yz + xz km/h xy 55. (b) Alier Aerge speed x+ y km/h (b) Disnce coered in n h second is gien by sn u+ (n ) Gien : u, g g 7g s4 ( 4 ) g 9g s4 7 s5 ( 5 ) s (c) Le PQ s nd L is he midpoin of PQ nd be elociy of he cr poin L. Using hird equion of moion, we ge (4) () s (4) () 5 Or s s s Also, () 5 Or () s s using Eq. (i) Or 5 km/hr 5...(i)

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor.

1. Consider a PSA initially at rest in the beginning of the left-hand end of a long ISS corridor. Assume xo = 0 on the left end of the ISS corridor. In Eercise 1, use sndrd recngulr Cresin coordine sysem. Le ime be represened long he horizonl is. Assume ll ccelerions nd decelerions re consn. 1. Consider PSA iniilly res in he beginning of he lef-hnd