02. MOTION. Questions and Answers

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1 CLASS MOTION Quesions and Answers PHYSICAL SCIENCE 1. Se moves a a consan speed in a consan direcion.. Reprase e same senence in fewer words using conceps relaed o moion. Se moves wi uniform velociy. 2. Disance Vs ime graps sowing moion of wo cars A and B are given. Wic car moves fas? s Speed = = slope of e grap Car A ravels more disance in less ime. I represens e slope of e curve of i. So car A moves fas. 3. Derive e equaion for uniform acceleraed moion for e displacemen covered in is n second of is moion. Disance ravelled in seconds S = u + a2 Disance ravelled in n seconds = un + an2 Disance ravelled in (n-1) seconds -1 = u(n-1) + a(n-1)2-1 = un u + a(n2-2n+1) -1 = un u + an2 -an+ a Disance ravelled in n second = - -1 = u + an - a = u + a(n - ) or u + a(2n-1) 4. A body leaving a cerain poin O moves wi an a consan acceleraion. A e end of e 5 second is velociy is 1.5 m/s. A e end of e six second e body sops and en begins o move backwards. Find e disance raversed by e body before i sops. Deermine e velociy wi wic e body reurns o poin O? Visi a : igniepysics.weebly.com u 1.5m/s 0 m/s O 5 s 6 s V = u + a Le iniial velociy = u m/s Acceleraion = -a m/s 2 (velociy decreases) A e end of 5 second V = 1.5 m/s 1.5 = u + (-a)5 1.5 = u 5a.. (1) A e end of 6 second V = 0 m/s 0 = u + (-a)6 0 = u 6a u = 6a. (2) subsiue (2) in (1): 1.5 = 6a -5a a = 1.5 m/s 2 from (2): u = 6a = 6(1.5) = 9 m/s Disance ravelled by body before i sops (Disance ravelled in = 6 seconds) S = u + a2 S = (9)6 + (-1.5)62 = 54 - (-1.5)18 = S = 27 m Wen e body reurns o poin O u = 0 m/s ; a = 1.5 m/s 2 ; = 6 s Final velociy V = u + a = (6) = 9 m/s (in opposie direcion) So V = -9 m/s 5. Disinguis beween speed and velociy. Speed Velociy 1 Te disance ravelled by e 1 Te displacemen of e body in uni ime. body in uni ime. 2 I is a scalar. 2 I is a vecor. 3 Is value is always posiive or zero. 3 Is value may posiive or zero or negaive. 4 Speed = 4 Velociy =

2 6. Wa do you mean by consan acceleraion? If a body ravels in sraig line and is velociy canges (increase or decrease) by equal amoun in equal ime inervals, Ten e acceleraion is said o be uniform acceleraion or consan acceleraion. 7. A poin mass sars moving in a sraig line wi consan acceleraion a. A a ime afer e beginning of moion, e acceleraion canges sign, wiou cange in magniude. Deermine e ime from e beginning of e moion in wic e poin mass reurns o e iniial posiion. A a Le a paricle sars a poin A Te iniial velociy u = 0 m/s Acceleraion = a m/s 2 Displacemen = S aken o ravel from A o B = sec According o firs equaion of moion Final velociy V = u + a V = 0 + a V = a.(i) According o second equaion of moion Displacemen S = u + a2 S = 0() + a2 S = a2 (ii) Afer ime, e paricle reurned. A -a B Le a paricle reurns a poin B Te iniial velociy u = a m/s Acceleraion = - a m/s 2 Displacemen = - S aken o ravel from B o A = I sec According o second equaion of moion Displacemen S = u + a2 - S = (a)( I ) + (-a)(i ) 2 - S = a I - a(i ) 2 From (ii) we ge - a2 = a I - a(i ) 2 B - 2 = I - (I ) 2-2 = 2 I - ( I ) 2 ( I ) 2 2 I - 2 = 0 Tis is in e form ax 2 + bx + c = 0 x = ± I = () ±() ()( ) () I = ± I = ± ± I = I = + 2 Toal ime aken for ravel = + I = = = (2 + 2 ) 8. Consider a rain wic can accelerae wi an acceleraion of 20cm/s 2 and slow down wi deceleraion of 100 cm/s 2. Find e minimum ime for e rain o ravel beween e saions 2.7 km apar. If a body saring from res, acceleraes a e rae α for some disance and deceleraes a e rae β and comes o res afer seconds. Average acceleraion a = α = 20 cm/s 2 ; β = 100 cm/s 2 ; =? Disance S = 2.7 Km = cm u + a2 = () + 2 = = = = 2700 x 12 2 = = 180 sec 9. A rain of leng 50m is moving wi a consan speed of 10m/s. Calculae e ime aken by e rain o cross an elecric pole and a bridge of leng 250 m. Leng of rain = 50 m Leng of bridge = 250 m Speed of rain = 10 m/s In case of crossing an elecric pole: Disance = leng of rain = 50 m = = = 5 sec.

3 In case of crossing a bridge: Disance= leng of rain + leng of bridge = = 300 m = = = 30sec. 10. Correc your friend wo says, Te car rounded e curve a a consan velociy of 70 km/. Wile a body is moving along a curved pa, e direcion canges coninuously. So we sould use speed insead of velociy. Te correc saemen is Te car rounded e curve a a consan speed of 70 Km. 11. Suppose a e ree ball s sown in figure sar simulaneously from e ops of e ills. Wic one reaces e boom firs? Explain. Te pa wic is o be ravelled by e ball is sor in firs ill. So e ball from e op of e firs ill reaces e ground. 12. Wen e velociy is consan, can e average velociy over any ime inerval differ from insananeous velociy a any insan? If so, give an example; if no explain wy? Consan velociy means bo magniude and direcion are consan. If velociy is consan, e average velociy over any ime inerval is equal o insananeous velociy a any ime. V = V 13. Can e direcion of velociy of an objec reverse wen i s acceleraion is consan? If so give an example; if no, explain wy? In case of verically projeced body; a e maximum eig of e body, e velociy is zero. I falls freely. I means is velociy was reversed. Acceleraion due o graviy is consan and is value is 9.8 m/s As sown in figure, a poin raverses e curved pa.draw e displacemen vecor from given poins A o B. Visi a : igniepysics.weebly.com Displacemen is e sores disance in a specified direcion. Displacemen vecor from A o B is denoed wi AB. 15. Draw e disance Vs ime grap wen e speed of a body increases uniformly Te disance ime grap for a body wic is moving wi speed increases gradually is as follows. Disance 16. Draw e disance ime grap wen is speed decreases uniformly. Te disance ime grap for a body wic is moving wi speed decreases gradually is as follows. Disance 17. You may ave eard e sory of e race beween e rabbi and oroise. Tey sared from same poin simulaneously wi consan speeds. During e journey, rabbi ook res some were along e way for a wile. Bu e oroise moved seadily wi lesser speed and reaced e finising poin before rabbi. Rabbi awoke and ran, bu rabbi realized a e oroise ad won e race. Draw disance Vs ime grap for is sory. Disance Hare and oroise sars a O. Tey reaced final desinaion in differen ime. OC represens e moion of oroise. OABD represens e moion of are.

4 18. Wa is e average speed of a Ceea a sprins 100m in 4sec.? Wa if i sprins 50m in 2sec? Case(i): disance = 100 m = 4 s Average speed = = = 25 m s Case(ii): disance = 50 m = 2 s Average speed = = = 25 m s 19. A car ravels a a velociy of 80 km/ during e firs alf of is running ime and a 40 km/ during e oer alf. Find e average speed of e car. Le us assume a e car ravels for 2 ime. for firs ours Disance = velociy x ime = 80 x = 80 Km for second ours Disance = velociy x ime = 40 x = 40 Km Toal disance ravelled = = 120 Km Toal ime = 2 ours Average speed = = = 60 Km 20. A car covers alf e disance a a speed of 50 km/ and e oer alf a 40km/. Find e average speed of e car. Le us assume a Te oal disance is = 2s Km For ravelling firs s disance speed = 50 Km = = ours For ravelling nex s disance speed = 40 Km = Toal disance ravelled = 2s Km Toal ime = + Average speed = = ours = rs = = = Km 21. A paricle covers 10m in firs 5s and 10m in nex 3s. Assuming consan acceleraion. Find iniial speed, acceleraion and disance covered in nex 2s. Visi a : igniepysics.weebly.com Iniial velociy = u m s Toal disance S = 20 m Toal ime = 8 sec Consan acceleraion = a m s 2 for 8 seconds S = u + a2 20 = u(8) + a(8)2 20 = 8u + 32a 2u + 8a = 5 (1) for firs 5 seconds S = u + a2 10 = u(5) + a(5)2 10 = 5u + a 20 = 10u + 25a 2u + 5a = 4 (2) Do (1) (2): 3a = 1 a = m s 2 (acceleraion) Subsiue is value in (1) 2u + 8( ) = 5 2u = 5 - ( ) 2u = u = m s (iniial velociy) Disance ravelled in nex 2 seconds = S 10 S 8 = (10) + ( )(10)2 (20) = + (20) = 20 = = 8.33 m 22. A car sars from res and ravels wi uniform acceleraion α for some ime and en wi uniform reardaion β and comes o res. Te ime of moion is. Find e maximum velociy aained by i.? B(V B = V max ) Velociy α O A 1 2 C (V A = 0) (V C = 0) Velociy a A (saring) = V A = 0 Velociy a B (maximum velociy) = V B = V max Velociy a C (ending) = V C = 0 Acceleraion = Le α is e acceleraion from A o B and β is e deceleraion from B o C β

5 α = β = = = = = 1 = 2 = Le Te oal ime aken by e car for acceleraion and deceleraion is. = = + = V max + = V max V max = 23. A man is 48m beind a bus wic is a res. Te bus sars acceleraing a e rae of 1 m/s 2, a e same ime e man sars running wi uniform velociy of 10 m/s. Wa is e minimum ime in wic e man caces e bus? A B C 48 x Man Bus. Iniial velociy of man u m = 10 m/s Iniial velociy of bus u b = 0 m/s Acceleraion of man a m = 0 m/s 2 (uniform velociy) Acceleraion of bus a b = 1 m/s 2 Le man sars a A and bus sars a B And man caces e bus a C. Bus ravels a disance x before cacing. for e bus S = u + a2 x = (0) + (1)2 x = 2..(1) Man is 48m beind e bus. He ravels (48+x) meers before cacing. for e man 48 + x = (10) + (0) x = 10...(2) Subsiue (1) in (2): = = = = 0 (-12) -8(-12) = 0 (-12)(-8) = 0-12 = 0 (or) -8 = 0 = 12 (or) = 8 Minimum ime for cacing e bus is 8 s. Visi a : igniepysics.weebly.com 24. Two rains, eac aving a speed of 30km/, are eaded a eac oer on e same rack. A bird flies off one rain o anoer wi a consan speed of 60km/ wen ey are 60km apar ill before ey cras. Find e disance covered by e bird and ow many rips e bird can make from one rain o oer before ey cras? Two rains are ravelling opposie o eac oer on e same rack. Speed of eac rain = 30 Km/ Relaive speed of rains = = 60 Km/ Te disance beween wo rains = 60 Km = Te aken for rain o reac ogeer = = 1r Te speed of bird = 30 Km/ Relaive speed of bird wi respec o rains =60+30=90 Km/ Te ime o fly from firs rain o second rain = (firs alf rip) = 1 = = ours Te disance ravelled by wo rains in ours = relaive speed x ime = 60 x = 20 x 2 = 40 Km Te disance beween wo rains afer ours =60 40=20 Km Te ime o fly from second rain o firs rain (second alf rip) = 2 = = ours = ours Te disance ravelled by wo rains in ours = relaive speed x ime = 60 x = 20 x = Km Te oal ime for one rip o bird = = + = + = ours = ours Te disance beween wo rains afer ours (one rip) = 20 = Km Te ime o fly from firs rain o second rain (ird alf rip) = 3 = = ours = ours Te disance ravelled by wo rains in ours = relaive speed x ime = 60 x = 20 x = Km Te disance beween wo rains afer ours = = Te ime o fly from second rain o firs rain (four alf rip) = 4 = / = ours ours Te disance ravelled by wo rains in ours = Km = relaive speed x ime = 60 x = 20 x = Km Te oal ime for second rip o bird = = + = + = ours = ours Te ime aken o bird for ravel successive alf rips are ours, ours, ours, ours, Te ime aken o rains o reac ogeer = 1 our Te ime for n alf rips o bird = 1 our = 1 [ ] = 1 [ [ ] = 1 ] = = 1 = 0 n = infinie value. So e bird can make infinie alf rips. Means infinie rips.

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