Kinematics Questions and Answers

1 A taxi driver moving at a velocity of 10 m s realised that he had 35 seconds to get to his destination which is 800 m away He therefore at 3m s2 for the rest of the accelerated journey Did he succeed in getting to his destination on time 5 P

Figure shows a particle starting from point A travelling upto B with a speed S then upto point C with a speed 2S and finally upto A with a speed 3S then its average speed for complete motion is Question Type Single Correct Type 1 2 120 3 1 2 S 1 8 S 2S

Two small rings O and O are put on two vertical stationary rods AB and A B respectively One end of an inextensible thread is tied at point A The thread passes through ring O and its other end is tied to ring O Assuming that ring O moves downwards at a constant velocity VI determine the velocity v2 of the ring 0 when ZAOO a 2sin a 2 A v C vi COSCE 3 cos a 2 2 cos a 2 sin a D None of these B Vi R 0

Jestion No 13 police jeep is chasing culprit going on motorcycle The motorcycle crosses a turning at 20 m s The jeep follows at speed of 30 m s crossing the turning 6 secon man motor cycle If they travel at constant speeds how far from turning point jeep catches up the motorcycle O 40 m O 50 m O O 360 m 120 m

A rocket of mass m m is launched with a velocity whose horizontal and vertical components are u and u At the highest point in its path the rocket explodes into two parts of mass m and m that separate in a horizontal direction in the original plane of motion Show that the fragments strike the ground at a distance apart given by U 2 m m K 1 9 M M2 where K is the kinetic energy produced by the explosion Neglect air resistance the mass of the explosive any spinning motion of the fragments and assume g is constant D

Consider oblique impact of a smooth sphere on a fixed plane According to Newton s experimental law of impact the velocity of rebound is proportional to the velocity of approach Express this statement in the form of an equation Write down also the equation required by conservation of momentum

A particle is subjected to two equal forces along two different directions If one of them is halved the angle which the resultant makes with the other is also halved The angle between the forces is A 45 B 60 C 90 D 120

282 A batsman hits a sixer and the ball touches the ground outside the cricket ground Which of the following graphs describes the variation of the cricket ball s vertical velocity with time between the time t as it hits the bat and time 2 when it touches the ground AMU Med 2001 4 H N D 1 2 d a b ffect

A motorboat sets out at 10 am from a position 6i 2j km relative to a marker buoy and travels at a constant speed of 53km h to intercept a ship The ship maintains a steady velocity vector 3i 4j km h and at 11 am is at a position 3 j km relative to the buoy Find the velocity vector of the motorboat the time of interception and the position vector of the point of interception relative to the buoy

30 A projectile is thrown with an initial velocity a b ms where and are the unit vecto along horizontal and vertical directions respectively If the range of projectile is twice the maximum height reached by it then a b 2 b b a c b 2a d b 4a 31 A uniform wire of length 20 m and weighing 5 kg hangs vertic

5 A ball moving with a speed of 9 m s strikes an identical stationary ball such that after the collision the direction of each ball makes an angle of 30 with the original line of motion The speeds of two balls after the collision is a 3 ms 3 ms c 3 3 ms 3 ms b 3 3 ms 3 3 ms d 3 m s 3 3 m s

A small block of mass m slides down on a ramp at inclination angle a with the horizontal The coefficient of frict between block and ramp is 4x where x is the distance through which the block slides The distance covered by the block before stopping would be tana 1 2 tana 2 2 3 tana 4 4 tana

2 7 A motorcycle and a car start from rest from the same place at the same time and travel in the same direction The motorcycle accelerates at 1 0 m s to a speed of 36 km h and the car at 0 5 m to a speed of 54 km h The time at which the car sup 2 ms up would overtake the motorcycle is a 20 s b 25 s c 30 s d 35 s

A stone is thrown from the top of a tower of height 50 m with a velocity of 30 m per second at an angle of 30 above the horizontal Then 1 the time during which the stone will be in air and 11 the distance from the tower base to where the stone will hit the ground are respectively A 3 sec 50 3 m B 4 sec 60 3 m C 5 sec 75 3 m D None of these

4 An infinite horizontal square grid of side a made of uniform material has current i fed into it at node A and this current leaves at B The semi infinite wires used for the entry and exit of current into this grid are shown in the figure 2 which is an enlarged version not drawn to scale of the grid in the locality of AB when observed along its plane The feeding wires are parallel to AB and just above the plane of the grid by a small distance 8 80 These feeding wires are thus not visible in figure I Consider an Amperean circular loop with AB as axis midpoint of AB as its centre and R as its radius as shown in figure 2 C is the midpoint of a square formed by AB as its side shown in figure 1 Take R Top view A A X Figure 1 Hol 2 B 484 a A R 0 Figure 2 Magnitude of circulation B de around the shown Amperean loop if B is taken due to grid and feeding wires is x B Magnitude of circulation B d7 around the shown Amperean loop if B is taken of due to entire grid excluding the feeding wires is y Magnitude of B at point C is z Then B y Hoi C y Hoi to abuting X D z z

2 Which of the following curve does not represent Boyle s law log P 0 45 and P a c By log P 135 log V b d PV log V V

A rocket is fired vertically from the ground It moves upwards with a constant acceleration 5 m s for 10 seconds after w the fuel is consumed Maximum height from ground upto which the rocket goes is Take g 10 m s 1 200m 2 325m 3 375m 4 425m A metal ring of mass m and radius R is placed on a smooth horizontal table and is set rotating about its own

37 On a two lane road car A is travelling with a speed of 36 km h Two cars B and C approach car A in opposite directions with a speed of 54 km h each At a certain instant when the distance AB is equal to AC both being 1 km B decides to overtake A before C does The minimum required acceleration of car B to avoid an accident is 1ms 2 b 1 5 m s 2 c 2 ms 2 d 3 ms 2

A ball is thrown from the top of a tower with an initial velocity of 10 m s at an angle of 30 above the horizontal hits the ground at a distance of 17 3 m from the base of the tower The height of the tower g 10 m s will be A 10 m C 110m B 12 m D 100 m

Consider the Atwood s machine shown in Fig 8 21 The masses are m and 2m and the pulley is a uniform disk of mass m and radius r The string is massless and does not slip with respect to the pulley Find the acceleration of the masses Use conservation of energy 16 2m Please help with a step by step process using conservation of energy I realized that K 1 2 mv 2 1 2 2m v 2 1 2lw 2 but that s as far as I got And the answer is v sqarroot 2ad holds here so we obtain a 2g 7 Thank you

a length c time b mass d angle 9 Two cars are travelling towards each other on a straight road with velocities 10 m s and 12 m s respectively When they are 150 m apart both drivers apply their brakes and each car decelerates at 2 m s2 until it stops How far apart will they be when they have come to rest a 89 m b c 108 m 98 m d 150 m

10 Block 1 of mass m is moving with speed u to the right on a horizontal surface of negligible friction as shown in the figure Block 1 makes an elastic head on collision with block 2 of mass 2m which is at rest Which of the following are correct velocities v and v for blocks 1 and 2 respectively immediately after the collision A v v and v U C v 0 and v E v E F A P 1 20 C 0 E 60 and U 1 201 M B v v and v D v v 11 A figure skater is spinning with her arms outstretched such that her rotational inertia is I She is spinning with an angular speed She pulls in her arms such that her rotational inertia reduces to I Her new angular speed will be 3 v and v B 2 v U D 300 12 A wheel of radius 15 cm has a rotational inertia of 2 3 kg m The wheel is spinning at a rate of 6 5 revolutions per second A frictional force is applied tangentially to the wheel to bring it to a stop The work done by the torque to stop the wheel is most nearly A zero C 100 I E 3840 J B 50 J D 1920

Pactice Paper 2 10 A particle is projected vertically upwards and it reaches the maximum height H in time T seconds The height of the particle at any time I will be 4 8 1 77 b H g t T 801 77 d H g t 1 If a body placed at the origin is acted upon by a 2k then which of the following 15 16 a T L

c 5i 9j 3 A particle of mass 0 1 kg is held between two rigid supports by two springs of force constant 8 N m and 2 N m If the particle is displaced along the direction of length of the springs its frequency of vibration is 8 a c SIK NIK 2 5 2 Hz 1111100 Hz d What is the wavelength of wave shown in given 8 b 7 Hz Hz c If E M moment then E M a leng c tim

Consider the acceleration of a particle along a straight line with an initial position of 0 m and an initial velocity of O m s a What is the velocity at 4 s Answer in units of m s b Find the position after the first 7 s Answer in units of m c How far did the particle travel from 7 s to 9 s Answer in units of m d Calculate the magnitude of the particle s average velocity from 1s to 9 s acceleration m s 6 4 s 2 O To 0 1 2 Answer in units of m s 3 4 5 time s LO 6 7 8 9

A small pebble is dropped off a 100 0 meter building a How long does it take for the pebble to reach the halfway point between the rooftop and the ground 50 0 b How long does it take for the pebble to reach the ground c Find the velocity of the pebble at the halfway point and right before it strikes the ground Ignore friction and air resistance for this problem

A particle moving along a straight line has velocity v m s when it covers a distance x along positive x axis The relation between two quantities is v 49 x When the velocity of particle is 1 m s its acceleration will be 01 m s 07 m s 02 m s O 0 5 m s

N in a moving particle from 2i 7j 4k m to 5i 2 j 8k m D What is the percentage increase in momentum if Kinetic energy of a body increases by 125 constant 45 A tungsten wire of length 20 cm is stretched by 0 1 cm Find the strain on the wire 46 If an iron wire is stretched by 1 Find the strain

A car and a bus left Regina at the same time The car drove 480 km west to Calgary The bus drove 570 km east to Winnipeg The bus travelled 15 km h faster than the car The car and the bus arrived at their destinations at the same time What were the speeds of the car and the bus 4

5 Two cars A and B cross a point P simultaneously with velocities 10 ms 1 and 15 ms 1 After that they move with different uniform accelerations and the car A overtakes B with a speed of 25 ms 1 What is velocity of B at that instant 2 25 ms 1

A man standing between two parallel hills dap his hand and hears successive echoes at repl intervals of 1 s If velocity of sound is 340 ms the distance between the hills is a 100 m c 510 m b 170 m d 340 m d 4L and 58 The transves as both end y x t

58 An aeroplane is flying with the speed of 100 m s towards east if the wind is blowing with the velocity 25 m s w r t ground southwards total speed of the plane is a V 100 m s b V 101 m s c V 100 m s d V 125 m s 9 A boat man could row hi

45 A projectile fired with initial velocity u at some angle 0 has a range R If the initial velocity be doubled at the same angle of projection then the range will be a 4R d R b 8R c R 4

65 1 109 1 10 920 ero Calculate power generated by tension in the string in first 2 seconds of motion 1 250 W P F V P F V 2 500 W 3 750 W 4 1000 W 150 10 15000 10 9 1 10 2aL 2 17 149

A mass of m kg is subjected to a constant force of F kg wt for t sec initially the body is being at rest Under the action o force the body moves a distance x metres in t secs and aquires a velocity of V m s Then x is

1 A particle of mass 1 Kg moves along X direction with a constant velocity 2 ms A force of 2N is applied on it along Y direction Velocity of the body 4 seconds after the force is applied 1 34 ms 3 4 17 ms 1 4 2 17 ms 1 2 3 34 ms 1

A vehicle having a mass of 1000 Kg is moving with a uniform velocity of 20 ms Sand is dropped into it at the rate of 5 Kg min The force needed to keep the vehicle moving with uniform velocity is 1 3N 2 SN 4 N 315 3 N

15 On a road going out of a city lights of the last traffic signal glow green for 10 min and red for 2 0 min After the traffic signal the road is straight and vehicles run at their constant speeds that lie in the range 60 km h to 80 km h This mode of operation of traffic lights causes the vehicles to come out of the city in groups Some distance away from the traffic signal these groups merge and become indistinguishable Assuming that the vehicles acquire their constant speeds after the traffic signal in negligible time which of the following conclusions can you make a The groups become indistinguishable 4 0 km after the traffic signal b The groups become indistinguishable 8 0 km after the traffic signal c Wider is the range of speed of the vehicles greater is the distance where the groups become indistinguishable d Larger is the number of fast moving vehicles shorter is the distance where the groups become indistinguishable

Questions 29 to 31 are based on the following physical situation A hot air balloon of constant ascent velocity can be used to investigate wind velocities at various altitudes Employing this idea one day a hot air balloon was released at a distance 1 100 m from a point where a telescope was installed to track the balloon Since wind velocity was almost zero up to a height of approximately 30 m that day the balloon first rose upwards and then due to horizontal drift caused by the wind it followed a plane curvilinear path During continuous tracking of the balloon the telescope has been rotated in a vertical plane without change in azimuth A graph depicting how the angle of elevation varies with time thus obtained is shown in the figure 29 Ascent velocity of the balloon is closest to a 2 67 m min c 8 m min 30 Wind velocity at the altitude of the balloon where angle of elevation acquires its maximum value is closest to a 4 m min c 8 m min b 6 m min d Information is insufficient to decide a 180 m c 300 m 31 Horizontal drift of the balloon when angle of elevation acquires its maximum value is closest to b 6 m min d 10 m min a 3 s t 9s c 11 s t 17 s b 200 m d Insufficient information Questions 32 to 35 are based on the following physical situation Two particle A and B are moving towards each other on a straight line with equal speeds 5 m s At an instant that is assumed t 0 s distance between the particles is 100 m It is desired to move another particle C always maintaining a distance 40 m from the particle A and 30 m from the particle B 2 When and for how long can the particle C fulfil the given condition b 9 s t 11 s d 3 s t 17 s 3 What is speed of the particle C at the instant t 5 s a 3 5 m s c 5 m s b 4 8 m s d 6 m s What is modulus of acceleration of the particle C at the instant t 5 s a 2 3 m s2 b 0 58 m s c 0 90 m s d 3 30 m s2 01 53 15 3 35 50 t min

One ball is dropped from a height of 200 feet After one second second ball is dropped from a height of 150 feet Which ball hits the ground first a First ball b Second ball c Neither first nor second ball d none

12 A cylindrical pipe of radius r is rolling towards a frog sitting on the horizontal ground Centre of the pipe is moving with a constant velocity v To save itself the frog jumps off and passes over the pipe touching it only at the top Denoting air time of the frog by T horizontal range of the jump by R and acceleration due to gravity by g which of the following conclusions can you make a T 4 r g c R 4 gr v r b T 4 g d R 4 gr v ar

A body released from a height falls freely towards earth Another body is released from the same point exactly two second later The separation between them two seconds after the release of the second body is 1 9 8 m 2 49 m 3 58 8 m 4 19 6 m

A rope of length L lies in a heap on a table except for a very small piece at one end whic hangs down through the hole Assume that the rope is greased so that it has no friction with itself This piece is released and the rope slides down through the hole The speed the rope at the instant it loses constant with the table is agL Find a Your Answer 1

A body is projected vertically upward from the surface of the earth the speed time graph is 1 V J j j j 4

A particle is projected at point A from an inclined plane with inclination angle 0 as shown in figure The magnitude of projection velocity is u and its direction is perpendicular to the plane After some time it passes from point B which is in the same horizontal level of A with velocity V Then the angle between u and will be 1 T 3 20 A u 0 B Ground 2 20 4 90 0

placem T 240 0 240 RUC ocity of both should a finite to the 300 250 200 150 AI DUAL CAMERA Shot by Souradeep Manna ocity DOP al to city at 100 50 0 0 18 s 20 s 4 8 2 4 of 2 4 E 4 8 7 2 9 0 12 0 2 a 4 10 12 14 16 Fig 3 3 Position time graph of a car 0 24 ms 20 18 s a 246 8 10 12 14 16 18 20 22 t s anges e this te of Fig 3 8 Acceleration as a function of time for motion me represented in Fig 3 3 Shot by Souradeep Manna RADUAL CAMERA Istantaneous acceleration is defined in the same way as the instantaneous velocity idea Positive a v Vo t 0 12 m s h x toamij neiz or v vo at Negative a b 0 N a 0 18 3 6 with 20 t s 2021 2021

4 If a particle moves in a straight line such that its position varies with time as x 5 2 6 t 2 then initial acceleration is Assume all quantities in SI units 1 6 m s2 3 12 m s2 2 5 m s 4 3 m s

A train is moving with a velocity of 90 km h It is brought to stop by applying the brakes which produce a retardation of 0 5 m s 2 Find i the velocity after 10 s and ii the time taken by the train to come to rest Ans i 20 m s ii 50 s S

5 A vehicle is accelerating on a straight road Its velocity at any instant is 30 km h after 2 s it is 33 6 km h and after further 2 s it is 37 2 km h Find the acceleration of vehicle in m s 2 Is the acceleration uniform Ans 0 5 m s Yes

Which of the following statements is a description of the motion of an object with changing motion Select one a Neither the speed nor the direction of motion of the object is changing O b The direction of motion of the object is changing O c The acceleration of the object is zero O d The velocity of the object is constant