Kinematics Questions and Answers

n 6 f COSOFN vsing V A for minimum displacem d

If a fish is rising in water with 3 m s a bird is rising in air with 6 m s then speed of fish as seen by bird is water 4 3 A 15 4 m s C 9 m s B D 33 4 9 GRIRED 4 m s m s

A particle moves along the sides AB BC CD of a square of side 25 m with a velocity of 15 m s Its average velocity is a 15 m s 1 b 10 ms 1 c 7 5 m s 1 d 5ms 1 www

2 What is the work done by the field of a nucleus in a complete circular orbit of the electron and what if the orbit is elliptical

2 A ball A is dropped from the top of a building and at the same time an identical ball B is thrown vertically upward from the ground When the balls collide the speed of A is twice that of B Collision occurs at a fraction of the height of the building is 212 2 215 2 137 2

5 An elevator car whose floor to ceiling distance is 2 7m starts ascending with a constant acceleration of 1 2 ms 2 2 s after the start a bolt falls from the ceiling of the car The free fall time of the bolt is g 9 8 ms 2 2 7 a b 9 8 S 5 4 9 8 S c 5 4 8 6 S d 5 4 V 11 S

A locomotive of mass m starts moving so that its velocity vari according to the law v a s where a is a constant and s is t distance covered Find the total work performed by all the fore which are acting on the locomotive during the first t seconds after t beginning of motion

Two point charges q each are placed at a distance R from each other in vacuum The force between them is F One of the charges is spread uniformly over the surface of a hemispherical bowl of radius R while the other is spread uniformly over the R r and both have a volume of a sphere of radius r common centre O The force on the sphere is nF then find the value of n

37 For a particle moving under the action of a variable force kinetic energy position graph is given then KA A B C D X 1 At A particle is decelerating 2 At B particle is accelerating 3 At C particle has maximum velocity

7 Under usual notations which of the following expressions represents equation of trajectory of an oblique projectile 1 y xsin0 1 anel 1 A R 3 y xtane 1 0 1 1 R 2 y x cose 1 4 y xsine 1 x R

E 0 A body is dropped from the roof of a multi storied building It passes the ceiling of the 15th storey at a speed of 20m s If the height of each storey is 4m the number of storeys in the building is take g 10ms and neglect air resistance 1 20 2125 n

A fixed re coilless cannon fires a shell with a speed at the same instant a man falls from rest from point O The shell hits a point on the wall Initially shell is aimed towards a point P as shown in figure Mark the incorrect option s b A The falling man sees the shell move along straight line directed along initial velocity Toe b Vo coseo C For a stationary man shell will strike below P 1 b tan 00 v B Time taken to reach wall is T g D Man falls through y 2 till the shell hits wall

20 21 22 Ram in his Santro accelerates at the rate of 31 21 m s while Shyam in his Maruti accelerates a 61 21 m s They both start from rest at the origin of an xy coordinate system After 5s What is Ram s speed with respect to Shyam A 15 m s C B 20 m s How far apart are they A 37 5 m B 50 0 m What is Ram s acceleration relative to Shyam A 5 m s B 4 m s C 25 m s C 62 5 m C 3 m s D 10 m s D 25 0 m D 1 m s C

5 A car starts from rest and accelerates uniformly for 10 s to a velocity of 8 ms 1 It then runs at a constant velocity and is finally brought to rest in 64 m with a constant retardation The total distance covered by the car is 584 m Find the value of acceleration retardation and total time taken Ans 0 8 ms 05ms 2

If the speed position v x relation of a particle moving in a straight line is given as v a bx2 where a and b are constants then the acceleration of the particle is proportional to 1 A on of the pa 2 x 3 X

Example 5 7 A moves with constant velocity u along then x axis B always has velocity towards A After how much time will B meet A if B moves with constant speed V What distance will be travelled by A and B 12 AD Fig 5 183

66 Two cars are moving in same direction with a speed o 30 km h They are separated by a distance of 5 km Wha is the speed of a car moving in opposite direction if it meet the two cars at an interval of 4 min a 60 km h b 15 km h c 30 km h d 45 km h

Comprehension Q 2 to Q 4 2 Two particles A B are projected from the same point in different directions in such a manner that their vertical components of initial velocities are same Which one of them will have more time of flight A A B B C Both will have same time of flight D cannot be determined Which one of them will have more range A A C same B B D cannot be determined Which of the following statements are correct about the motion A Both the bodies have the same maximum height B Both the bodies cross each other at some point of the motion C Both the bodies will have the same velocity at the maximum height D Both the bodies will land at the same place OB

3 A basketball player is running at a constant speed of 2 5 m s when he tosses a basketball upward with a speed of 6 0 m s How far does the player run before he catches the ball Ignore air resistance a 3 1 m b 4 5 m c The ball cannot be caught because it will fall behind the player d 6 0 m

57 Position time graph of a particle moving along straight line is shown which is in the form of semi circle starting from t 2 s to t 8 s Select the correct statement x m 0 0 2 5 8 t s 1 Velocity of particle between t 0 to t 2 sis positive 2 Velocity of particle is opposite to acceleration between t 2 to t 5 s 3 Velocity of particle is opposite to acceleration between t 5 to t 8 s 4 Acceleration of particle is positive between t 2 s to t 5 s while it is negative between t 5 s to t 8 s

A fishing boat is anchored 9 km away from the nearest point on the shore A messanger must be sent from the fishing boat to a camp 15 km from the point on shore closest to boat If the messanger can walk at a speed of 5 km per hour and can row at 4 km h determine the distance of that point in km from the camp where he must land so as to reach the camp in least possible time Boat 9 km Shore 15 lim Camp akm

If a ball is thrown vertically upwards with speed u the distance covered during the last t seconds of its ascent is a ut b 1 872

35 Ram moves with a velocity of 10 m s in west direction Shyar moves a direction 23 East of North Ram is 100 m away from Shyam in direction 53 East of North of him What should be speed of Shyam so that he collides with Ram A 4 3 m s B 10 m s C 12 m s To man running at a speed of 5 m sec the rain drops appear to be fallin D none of these

A particle projected vertically upwards attains a maximum height H 1 If the ratio of the times to attain a height h h H is then a 4h 3H 6 c 3h H b 3h 4H d 4h H 3

51 The speed time graph for a body moving along a straight line is shown in figure The average acceleration of body may be speed m s 20 1 0 3 4 m s 5 10 t s 2 4 m s 4 All of these

A spider is hanging by means of its own silk thread directly above a transparent fixed sphere of radius R 20 cm as shown in the figure The refractive index of the material of the sphere is equal to 2 and the height of the spider from the centre of the sphere is 2R 40 cm An insect initially sitting at the bottom starts crawling on the sphere along a vertical circular path with the constant speed of 4 cm s For how long time the insect will be invisible for the spider assume that it crawls once round the vertical circle A 80 sec 160 C sec 3 B 320 3 80 3 sec sec spide

figure a resistance coil wired to an external battery is placed inside a thermally insulated cylinder tted with a frictionless piston and containing an ideal diatomic gas A current i 200 mA exists in the bil which has a resistance R 350 52 If the pressure of the gas remains constant what should be the beed v in cm s of the piston of mass m 10 kg Take Patm 10 Pa A 10 cm H Coil 1

Starting from rest a train travels a certain distance with a uniform acceleration a Then it travels with a uniform retardation and finally comes to rest again If the total time of motion is t find 1 the maximum velocity attained and ii the total dis tance travelled by the train

20 Figure shows the graph of velocity versus time for a particle going along x axis Initially at t 0 particle is at x 3m Find position of particle at t 2s in m 46 v m s 10 2 O 8 t

A ball is projected at an angle of 45 so as to pass a wall at a distance a from the point o projection and falls at a distance b on the other side of the wall If h is height of wall then zab ab 6 B 1 h mb

H HAMPLE MPLE 15 A driver takes 0 20 s to apply the brakes after sees a need for it This is called the reaction time of the driver If he is driving car at a speed of 54 kmh brakes cause a deceleration of 6 0 ms 2 find the distanc travelled by the car after he sees the need to put the brakes 1 and the

30 The value of 1 1 3 3 T T is www XT A5 kg XT B5 kg XT C5 kg 2 2 4

Q 2 Interarrival time of pieces at the given flow shop is exponential with mean 10 minutes Operation time of M1 machine has Uniform distribution with a 3 and b 11 Operation time of M2 machine has Normal distribution with 5 ox 1 5 Calculate the average waiting time in queue and total machine idle time 15 p M1 M2

2 Which of the sets given below may represent the of three vectors adding to zero b 4 8 16 magnitudes a 2 4 8 c 1 2 1 d 0 5 1 2

25 All the graphs below are intended to One of them represent the same motion does it incorrectly Pick it up JEE Main 2018 Velocity Distance a c Position Position b Time d Time Velocity Time

C 550 m s D 660 m s B 55 m s A 110 m s A small block slides without friction down an inclined plane starting from rest Let S be the distance travelle S JEE 2004 Scr is from time t n 1 tot n Then Sn 1 2n 1 2n 1 2n 2n 1 2n 1 2n 1 A B C D 2n 2n 1 The velocity displacement graph of a particle moving along a straight line is shown

A particle is moving in a straight line and is observed to be at a distance a from a marked point initially to be at a distance b after an interval of n seconds to be at a distance c after 2n seconds and to be at a distance d after 3n seconds Prove that if the acceleration is uniform d a 3 c b and that the c a 2b acceleration is equal to n

13 If a vector OP 31 31 is turned clockwise by an angle of 15 then the y component of rotated vecto would be 1 2 9 3 2 9 3 2 2 2 2 4 9 2

A stone with weight W is thrown vertically upwards into the air with initial speed vo If a constant force f due to air drag acts on the stone throughout its flight a show that the maximum height reached by the stone is h v 2g 1 f W b show that the speed of the stone upon impact with the ground is v V W f W f 1 2

Density of wood is 0 5 g cc in the CGS system of units The corresponding value in MKS units is A 500 B 5 C 0 5 D 5000

A particle of mass m is acted upon by a force F given by R t If this law is to be tested experimentally by observing the motion starting from rest the best way is to plot 1 a log v t against t the empirical law F c log v t against 1 b v t against d log v t against t

4 A body moves in a two dimensional space with its position vector given by F 4t 3 i 3t 7 in m and t in seconds The initial velocity of the particle is a 4 ms b 10 ms 1 c 6t 4 ms e 4i ms

9 A car moving at a speed v is stopped in a certall distance when the brakes produce a deceleration a If the speed of the car was nv what must be the deceleration of the car to stop it in the same distance and in the same time a na c m b na d n a

A particle moves in xy plane with velocity V 2 t 1 where t in s gives v in m s The 4 particle starts from origin Find the y cordinate when the x coordinate becomes zero after start 8 1 5 2 2 m 24 3 4 8

At a height 0 4 m from the ground the velocity of a projectile in vector form is v 61 2jm s The angle of projection is g 10 m s2 1 45 2 60 3 30 4 tan 3 4

A projectile is fired at some angle 0 with speed v such that it crosses two walls of equal height symmetrically as shown The angle of projection with horizontal is 1 53 3 45 Y vertically beg t 2sn t 6s 0 120 m x 2 37 4 60 BS C 0

25 Find the tension T needed to hold the cart in equilibrium if there is no friction 1 3 Mg 10 Mg 2 T4 30 M 30 2 4 Mg 9 3 Mg 4

A cannon fires a shell with a speed of 84 m s When the cannon is inclined at 45 the horizontal distance covered is observed as 630 m What is the percentage decrease in the horizontal distance observed due to air resistance

m at XI 500 A rocket has a mass of 100 kg 90 of this is fuel It ejects fuel vapours at the rate of 1 kg sec with a velocity of 500 m sec relative to the rocket It is supposed that the rocket is outside the gravitational field The initial upthrust on the rocket when it just starts moving upwards is NCERT 1978 a Zero b 500 N c 1000 N d 2000 N

ragraph for question nos 26 to 28 Ram and Shyam are walking on two perpendicular tracks with speed 3 ms and 4 ms respectively At a certain moment say t 0 sec Ram and Shyam are at 20 m and 40 m away from the intersection of tracks respectively and moving towards the intersection of the tracks C During the motion the magnitude of velocity of ram with respect to shyam is A 1 ms B 4 ms C 5 ms 1 D 7 ms Shortest distance between them subsequently A 18 m B 15 m is C 25 m D 8m The time t when they are at shortest distance from each other subsequently is A 8 8 sec B 12 sec C 15 sec D 44 sec