Kinematics Questions and Answers

In adjacent figure a boy on a horizontal platform A kept on a smooth horizontal surface holds a rope attached to a box B Boy pulls the rope with a constant force of 50 N The coefficient of friction between boy and platform is 0 5 mass of boy 80 kg mass of platform 120 kg and mass of box 100 kg A B A Velocity of platform relative to box after 4 sec is 2m s B Velocity of boy relative to platform after 4 sec is 2m s C Friction force between boy and platform is 30 N Friction force between boy and platform is 50

94 A sphere of mass M is suspended by a metal wire of length I and diameter d When in equilibrium there is a gap of Al between the sphere and the floor The sphere is now gently pushed aside so that it makes and angle 0 with the vertical If E is the Young s modulus of the wire material the maximum value of 0 for which the sphere fails to rub past the floor is given by a sin 1 T d Al 8M gl b tan Ed Al 8M gl 1

A car is moving on a straight road The velocity of the car varies with time as shown in the figure Initially at t 0 the car was at x 0 where x is the position of the car at any time t Find acceleration of car at time t 15 sec and t 55 sec v m s 1 8 4 0 10 20 30 0 5 0 m s 2 50 60 70 t sec p navio 2 0 0 4 m s 3 0 0 4 m s 4 0 0 2 m s The acceleration time graph of a particle moving along straight line is as shown in the figure What is the velocity of the particle at t 8 sec if initial

A person pulls a 50 kg crate by 40 m along a horizontal floor by a constant force F 100 N which acts at an angle of 37 to the horizontal direction as shown in the figure The floor is rough and exerts a frictional force F 50 N Determine the net work done on the crate R 989 7 J 894 1 J 797 8 J mg L Pp 0 37 Test time left 30 40 m

Two small rings each of mass m are connected to the block of same mass m through an inextensible massless string of length l Rings are constrained to move over smooth rod AB Initially the system is held at rest as shown in Fig Let u and be the velocities of ring and block respectively when string makes an angle 60 with the vertical m m m B

A leather belt transmits 20kW power from a pulley of 750mm diameter which runs a 500 rpm The belt is in contact with the pulley over an are of 160 degrees and the coefficient of friction between the belt and the pulley is 0 3 Find the tension on each side of the open belt drive What is main purpose of lubrication State important properties of a good lubricant

For a certain tower of unknown height it is found that maximum range at a certain projection velocity is obtained for a projectile angle of 30 and this range is 10 3 m the projection velocity is A 10 3 m s B 5 3 m s C 10 m s D 5 m s

E A particle moves along a straight line OX At a time t in seconds the distance x in metres of the particle from O is given by x 40 12t t How long would the particle travel before coming to rest a 16 m b 24 m c 40 m d 56 m 2006

The ants of the North Creek Ant Colony traverse a straight trail between their colony and a nearby picnic table One ant returning after quenching its thirst with a portion of a tasty beverage dripping from the table is first observed along the trail 3 9 m from the colony Then after traveling a total of 1 8 m while staggering back and forth along the trail the ant falls unconscious 1 1 m from the colony exactly 41 s later Defining the entrance of the colony as the origin and the positive direction toward the picnic table determine the ant s average velocity vavg during this time interval

A fixed solid uniform mass density sphere has a thin tunnel along radius A point mass m is released from surface as shown Co efficient of restitution is e 1 16 maximum separation between point mass and centre of sphere after one collision is find n Consider mutual gravitational attraction R

3 Two particles A and B move with constant velocities v and At the initial moment their position vectors are and respectively The condition for particle A and B for their collision is 1 1 V V 2 3 V V H 1 1 V 2 1 22 2 0 4 V xV X

13 The de Broglie wavelength of a thermal equilibrium with heavy water at a temperature T Kelvin and mass m is 2h 2 3mkT h 4 TmkT h 1 3mkT 2h JmkT 3 44 19

4 Cannot be calculated 41 A stone falls from rest The total distance covered by it in 41 per farraren fire af sifa 4 Hand the last second of its motion is equal to the distance covered in the first three seconds What is the height from which the stone was dropped Take g 10 ms FOR ER FORRIT 1 25 m 2 100 m gt 3 125 m 4 200 m 1 25 m 2 100 m 3 125 m 4 200 m SCRE feng 10 ms 9 S xtoxy 45 9 2n 1 a SI S 1 X 5 X 5 XX IS 90 9 1 5

a A particle initially at rest moves from fixed point in a straight line so that its sing Show that at time seconds 1 acceleration at any time is 5 1 from start it is at a distance of 27 In 1 from the fixed point

footballer kicks a ball directly towards a wall 10m away and walks after the ball in the same direction at a constant speed 2m s The ball starts at 4m s but decelerates at a constant rate of 0 5m s 2 When it hits the wall it rebounds to travel away from the wall at the same speed with which it hit the wall a Find the time after initial kick when the ball returns to the footballer b what assumptions have been made in your answer

A boulder with mass mo is dropped from a stationary hovering helicopter from a height of ho ssuming that the quadratic air drag term dominates what if the velocity of the boulder as a functio me Take the downward direction to be positive The following integral might be helpful dx atanh x

1 1 3 3 2 2 4 1 and 3 27 The distance travelled by a particle is directly proportional 27 2 to t 2 where t time elapsed What is the nature of 122 motion 1 Increasing acceleration 2 Decreasing acceleration 3 Increasing retardation Decreasing retardation 8 For two particle A and R displacement S TY 2 S 1T 2 1 1 3 3 1 2 3 4 a 2 2 4 1 2 3

8 In bungee jumping a performer ties one end of an elastic cord with his feet and the other end to a fixed support on a very high place and then jumps off A bungee jumper of height h 1 5 m and mass m 66 kg has to jump from a tower of height H 62 5 m The bungee cord available is lo 30 m long and has a force constant k 33 N m If the minimum safe clearance from the ground is d 1 0 m what maximum length of this cord can the bungee jumper use

Quiz Which of the following velocity time graphs see box in the nex page matches the given acceleration time graph which you see at the right Time is plotted along the horizontal axis in all cases 2009 HAMN A A BB

Two forces are acting on an object One force of 50 0 N is acting at an angle of 30 degrees to the horizontal The other is acting at an angle of 90 degrees to the horizontal If the resultant force has a magnitude of 61 2 N acting at an angle of 45 degrees to the horizontal what is the magnitude of the second force

Graph between the square of the velocity v of a particle and the distance s moved is shown in figure The acceleration of the particle in kilometers per hour square is 0 02 2 S 1 2250 3 4600 km hr 2 900 2250 s km 900 0 6 2 3084 4 3084 5

Two trains start simultaneously from points A and B towards each other Each of them first moves with uniform acceleration the initial speeds of the trains are equal to zero the accelerations are different and then having attained a certain speed at different time moments uniformly The ratio of the speeds of the uniform motion of the trains is 4 3 At the time of their meeting the speeds of the trains were equal and they arrived at points A and B simultaneously Find the ratio of the accelerations of the trains The distance between

A person travels along a straight road for the first half time with a velocity v and the second half time with a velocity v Then the mean velocity V is given by ON V V2 2 217 02 1 1 V1 V O V V V V2

The acceleration of free fall at a planet is determined by timing the fall of a steel ball photo electrically The ball passes B and C at times t and t after release from A The acceleration of free fall is given by Point of release A 2h Light beam beam A und Photoelectric cell 2h D 2h

d a v v 29 The displacement x of a particle varies with time t as x ae at be t where a b a and are positive constants The velocity of the particle will 2005 a Be independent of B b Drop to zero when a c Go on decreasing with time d Co on is rish videre

A particle is thrown upwards from ground It experiences a constant resistance force which can produce retardation 2 m s The ratio of time of ascent to the time of descent is g 10 m s A 1 1 B 2 C 2 D KM0060

At t 0 an arrow is fired vertically upwards with a speed of 100ms A second arrow is fired vertically upwards with the same speed at t 5s Then g 10m s A the two arrows will be at the same height above the ground at t 12 5s B the two arrows will reach back their starting points at t 20s and t 25s C the ratio of the speeds of the first and second arrows at t 20s will be 2 1 D the maximum height attained by either arrow will be 1000m

A block starts from rest at the top of frictionless slide at a height h above the ground The block leaves the slide moving perfectly horizontally at a height he above the ground The block eventually hits the ground traveling at an angle 30 below the horizontal The ratio of hi and his h 3 380 0 3

of h meter vertically then maximum distance through which it can be thrown horizontally by the same person is 1 h 2 2 h 3 2h 4 3h 14 At the top of the trajectory of a projectile direction of its velocity and acceleration are 1 perpendicular to each other 2 parallel to each other 3 inclined to each other at angle of 45 4 antiparallel to each other 15 At the height 80 m an aeroplane is moving with 150m s A bomb is dropped from it so as to hit a target At what distance from the target should bomb be dropped 1 605 3 m 2 600 m 3 80 m 4 230 m 16 Three balls are dropped from the top of a building with equal speed at different angles When the balls strike ground their velocities are U 2 va respectively than 1 12 13 2 3 vy 3 V1 4 V2 V3 Vy 2 1280 m 1 29 10 3 1440 m 4 960 m 18 A cart is moving horizontally along a straight line with contant speed of 30 m s A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m At what speed relative to the cart must the projectile be fired given g 10m s 1 10 m s 2 m s 3 10 8 m s 4 None of the above 19 A cart is moving with speed of 20m s on a horizontal track A body is projected with speed 40m s relative to cart from the cart in such a way that path of body appear to be straight line for an observer on ground Time for which body remains in air is 1 2 3 sec 2 4 sec 3 4 3 sec 4 8 sec 20 A body is projected with speed u at an angle with the horizontal after what time it will start moving perpendicular to its initial direction of projection 1 t 2 t 3 t 9 sin 20 2x g sin W 29 sin 17 Fill OMR Sheet An object of mass 2m is projected with a speed of 100 m s at an angle sin to the horizontal At the highest point the object breaks into pieces of same mass m the first one comes to rest The distance between If above link doesn t work please go to test link from point of landing of the bigger piece is given g 10 m s where you got the pdf and fill OMR from there 11 9 sin 9

3 4 53 4 A body is projected with initial kinetic energy of 100 J and at an angle of 60 with the horizontal The K E of the body at highest point will be 1 25 J neet prep A V 1 sin 2 cos 3 sin 2 A smooth square platform ABCD is moving towards right with uniform speed u At what angle 8 must a particle be projected from A with speed v so that it strikes the point D Ankur Sir Live Session 13 Aug 2020 Contact Number 9667591930 8527521718 6000m u 250 m s Page 500m s

the same SI units 1 e m s S For a moving particle in a given interval of tim Average speed can be a many valued functio but average velocity would be always a singl valued function Par

The direction of motion of a projectile at a certain instant is inclined at an angle 60 to the horizontal After 3 seconds it is inclined an angle 30 If the horizontal component of velocity of projection is in m sec take g 10 m s er fr

A particle moves in a straight line its position in m as function of time is given by x at b What is average velocity in time interval t 3 sec to t 5 sec Where a and b are constants and a 1 m s b 1 m A 8 m s B 4 m s C 6 m s D zero

A particle moves along x axis in positive direction Its acceleration a is given as a cx d where x denotes the x coordinate of particle c and d are positive constants For velocity position graph of particle to be of type as shown in figure the value of speed of particle at x 0 should be 4d 3 2d 4 8d2

There are two inclined planes AO and OB inclined at 45 and 60 respectively with the horizontal as shown in figure When a man moves on the inclined plane AO he observes that the rain drops are failing at 45 with the vertical When the man moves on the inclined plane OB he observes that the rain drops are falling vertically downward Then actual speed of rain w r t ground is 1 5 2m s A 45 10m s 45 2 20 3m s O 60 B vertical 20m s fron horizontal 3 10 2m s 4 None of these

Both the cars are accelerating towards right and their initial velocity is also in rightward direction as shown in figure Maximum separation between car A and car B is a 1m s O 200 O 50 100 O 150 a 2m s car A 14 u 36km hr 100m car B u 72km hr

A particle is projected from ground from O with speed 20 m s making an angle 45 with ground Two high smooth and vertical walls are present one 10m ahead and other 15m behind the point of projection If collision of the particle with the walls are perfectly elastic then where will the particle land from the point of projection 1 5m ahead 2 5m behind 3 10m ahead 4 10m behind

The displacement time graphs of two moving particles makes angles of 30 and 45 with the time axis are shown below The ratio of their velocities is displacement A 3 2 B 1 1 C 1 2 D 1 3 450 30 time

A body of mass 1 kg starts from origin with initial velocity 81 101 m s If a constant force F 21 31 N acts on the body find the time in which x component of velocity becomes zero O 8 sec O2 sec O4 sec 10 3 sec

13 A piece of wire is bent in the shape of a parabola y kx y axis vertical with a bead of mass m on it The bead can slide on the wire without friction It stays at the lowest point of the parabola when the wire is at rest The wire is now accelerated parallel to the x axis with constant acceleration a The distance of the new equilibrium position of the bead where the bead can stay at rest with respect to the wire from the y axis is 1 2 3 4 gk 2gk Ayk

A body starting from rest is moving under a constant acceleration in straight line Suppose S is the displacement in first 10 sec S is the displacement in 5 the next 10 sec Find 5

Two small balls A and B are launched in the same vertical plane simultaneously with same speec of 20 m s at t 0 Ball A has an initial horizontal velocity and ball B has initial velocity at an angle E above the line joining A and B as shown If the projectiles collide in mid air at time t then O 8 45 O 0 60 O 8 30 O 8 37 100m 20 m s 100 3 m 20 m s B

An object is thrown horizontally from a point A from a tower and hits the ground 3s later at B The line from A to B makes an angle of 30 with the horizontal The initial velocity of the object is take g 10 m s O 15 3m s 15 m s O 10 3m s O 25 3m s 30 B

Prob 2 Consider the two vectors A and B Choose the incorrect option s about the magnitude of their sum i e A B if B Sol A is equal to A B C cannot be greater than A B A B A B cannot be less than A B D must be equal to A B A B B 2 A B eos 0 since 0 0 H 1 cos 0 1 Hence A B 2 A B B A B 2 A B Thus A BA B Alternately triangle inequality Hence A B D is incorrect

A boy walks on a straight road from his home to market 3 km away with speed of 6 km h He stays at market for 20 minute and returns home back at speed of 6 km per hour His average speed over round trip is

In the figure shown is given a flat plate and a rotating cone with a very acute angle e less than 5 The apex of cone just touches the plate surface A liquid with coefficient of viscosity n fills the narrow gap formed by the cone and plate Cone is rotated with angular velocity o as shown Neglect end effects and assume a linear velocity profile 1 A Velocity gradient in the liquid is 0 B Velocity gradient in the liquid is 0 C The torque on the driven cone is equal to D The torque on the driven cone is equal to R 700 H R R

In a battle field of ancient times a soldier with a catapult stationed on the top of a very high cliff notices camps of enemy close to the bottom of the cliff as shown in the figure Stones can be launched from the catapult with a speed u 40 m s at an angle 0 60 above the horizontal If the air resistance reduces speed of the stone at a rate k 0 1 m s m and there is no wind at what horizontal separation from the enemy camps should the soldier install the catapult to hit the enemy camps

A body with mass 5 kg is acted upon by a force F 3i 4 N If its initial velocity at t 0 is v 6i 12j ms then the time at which it will just have a velocity along x axis is 12 S 0 14 s O 10 s O 15 s

As we have discussed in article 6 3 that equations like v u at ve etc can be applied directly with constant or uniform acceleration Further in one dimensional motion all vector quantities displacement velocity and acceleration can be treated like scalars by using sign convention method In this method one direction is taken as positive and the other as the negative and then all vector quantities are written with paper signs In most of the cases we will take following sign convention The equations used in 1 D motion with uniform acceleration are v u at v u 2as ut 1 2 at s ut 1 So ut In horizontal 1 D motion ve ve In vertical 1 D motion Fig 6 10 S u at 2 In the above equations u initial velocity v velocity at time t a constant acceleration s displacement measured from the starting point ve iii iv v Here starting point means the point where the particle was at t 0 It is not the point where u 0 S displacement measured from any other point say P where P is not the starting point So displacement of the starting point from P s displacement not the distance in the second

An explosion blows a rock of mass 500 kg into three pieces Two pieces with masses 200 kg and 100 kg go off at right angle to each other with velocity of 8 m s and 12 m s respectively What is speed of third part O 10 m s 20 m s 28 m s O 14 m s