Kinematics Questions and Answers

In the figure two particles are launched from the origin of the coordinate system at time t 0 Particle 1 of mass m 5 80 g is shot directly along the x axis on a frictionless floor where it moves with a constant speed of 12 8 m s Particle 2 of mass m 3 20 g is shot with a velocity of magnitude 24 1 m s at an upward angle such that it always stays directly above particle 1 during its flight a What is the maximum height Hmax reached by the com of the two particle system In unit vector notation what are the b velocity and c acceleration of the com when the com reaches Hmax a Number i 5 M Units

Ship A is salling toward north east with velocity 7 301 50 km h where i points east and j north The ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards the west at 10 km h A will be at the minimum distance from Bin A B C 4 2 h 3 2 h 2 6 h Correct Answer

A gun throws a shell with muzzle speed of 98 m s When the gun is elevated at 45 the range is observed as 900 m Due to air resistance its range is decreased by A 160 m B 120 m C 80 m D 40 m

1 4 x 2 A ball is thrown upwards from a planet such that distance travelled in the 4th or 5th second is one forth of the distance travelled in the first two seconds of its downward journey If the maximum height attained by the ball is 32m choose the correct statement s Question Type Multiple Correct Type 2 English 3 Review Acceleration due to gravity of the planet is 2 m s Acceleration due to gravity of the planet is 4 m s Distance travelled by the ball in 4th second is 2m Time taken for the ball to strike around

2 A mass weighing 4 pounds stretches a spring 2 feet The mass is initially released from the equilibrium position wit an upward velocity of 1 ft s a Find an IVP that describes the motion of the mass b Determine a function that describes the position of the mass at any time

Q 15 A stone is thrown in a vertically upward direction with a velocity of 5 m s If the acceleration of the stone during its motion is 10 m s in the downward direction what will be the height attained by the stone and how much time will it take to reach there

In a car race of a straight path car A takes time t less than car B at the finish and passes finishing point with a speed v more than that of car B Both the cars start from rest and travel with constant acceleration a and a2 respectively Then v is equal to

A thief is running away on a straight road in jeep moving with a speed of 9 m s A police man chases him on a motor cycle moving at a speed of 10 ms If the instantaneous separation of the jeep from the motorcycle is 100 m how long will it take for the police to catch the thief 19 s A 1s C 100 s 90 s B D

73 Six persons of same mass travel with same speed u along a regular hexagon of side d such that each one always faces the other After how what will they meet each other 1 3 u 2d uf ud 2d 3u 4 d 3u 2

A shell is fired from canon with a velocity of 200 m s at an angle of 30 with the horizontal The horizontal range attained by it is g 10ms A 2 10 2 m 4 10 3 m C B 2 10 3 m D 2 x 10 3 m

options for the question below A ball of mass 2 kg moving with a velocity 12 m s collides elastically with a stationary body of mass 6 kg The final velocity of the 2 kg body is Options 0 0 0 0 6 m s 6 m s 12 m s 12 m s

When a particle moves with uniform velocity which of the following relations are correct 1 Average speed Average velocity ii Instantaneous speed Instantaneous velocity iii Distance covered Magnitude of displacement 1 i ii iii 2 i ii 3 ii iii 4 i iii 17

A ball is projected horizontally from top of a 80 m deep well with velocity 10 m s Then particle will fall on the bottom at a distance of all the collisions with the wall are elastic and wall is smooth A 5 m from A C 2 m from A B 5 m from B D 2 m from B 80m A 10m s 7m

A bomb of mass 4m is projected with velocity v at an angle 0 with horizontal At maximum height it explodes into two equal parts One part falls at point of projection Then at what distance from the point of projection other part will fall 1 3 2v sin 20 g 2 v sin 20 a 2 4 v sin 0 g v sin 0 2g

42 In the figure shown massolinu R of both the spherical body and block is m Moment of inertia of the spherical body about centre of mass is 2mR2 The spherical body rolls on the horizontal surface There is no slipping between any two surfaces in contact The ratio of kinetic energy of the spherical body to that of block is a 3 4 b 1 3 c 2 3 d 1 2 no no 2R

Velocity v versus displacement along a straight line is as shown in graph The corresponding plot of acceleration a as a function of displacement x is Ko X a t K a a X X3 X x plot of a body moving X X

9 A particle of mass 2m is projected at an angle of 45 with horizontal with velocity of 20 2 m s After 1s explosion takes place and the particle is broken into two equal pieces As a result of explosion one part comes to rest The maximum height attained by other part will be g 10m s 1 40m 3 30m 2 25m 4 35m

an historical movie two knights on horseback start from rest 72 9 m apart and ride directly toward each other to do battle Sir George s acceleration as a magnitude of 0 284 m s while Sir Alfred s has a magnitude of 0 337 m s Relative to Sir George s starting point where do the knights collide umber e tolerance is 2 Units m

A small ball is projected horizontally between two large blocks The ball is given a velocity Vms and each of the large blocks move uniformly with a velocity of 2Vms The ball collides elastically with the blocks If the velocity of the blocks do not change due to the collision then find out the velocity of the ball after the 2nd collision 1 1 Assume friction to be absent

An asteroid of mass M explodes into a spherical homogeneous cloud in free space Due to energy received by the explosion the cloud expands and the expansion is spherically symmetric At an instant when radius of the cloud is Ro all of its particles on the surface are observed receding radially away from the centre of the cloud with a velocity Uo What will the radius of the cloud be when its expansion ceases An 2GMRO M 1 Ro

n the figure all pulleys P1 P2 P3 are massless and all the blocks 1 2 3 are identical each having mass m The system consists of infinite number of pulleys and blocks Strings are light and in extension and horizontal surfaces are smooth Pulley P1 is moved to left with a constant acceleration ao The acceleration of block 1 will be Assume the strings to remain horizontal kao Find 2k a P P2 HEWITEM P3 FERMITTEN 3 ENTERT

58 A ball is projected vertically upwards with a certain speed Another ball of the same mass is projected at an angle 60 to the vertical with the same initial speed The ratio of their potential energies at highest points of their journey will be 1 1 1 2 2 1 3 3 2 4 4 1

In the figure all pulleys P1 P2 P3 are massless and all the blocks 1 2 3 are identical each having mass m The system consists of infinite number of pulleys and blocks Strings are light and in extension and horizontal surfaces are smooth Pulley P1 is moved to left with a constant acceleration c ao The acceleration of block 1 will be Assume the strings to remain horizontal kao Find 2k a T P2 P3 FERTITTEN FTTTTNITTEEN FREM

b What If If the temperature near the diff suddenly falls to 0 C reducing the speed of sound to 331 m s what would the initial speed of the rock have to be in m s for the soccer player to hear the sound of the splash 3 25 s after kicking the rock 15 09 x m s

A wrecking ball attached to the end of a long light chain is released from rest from a height H 5 meters off the ground as shown in the figure At the lowest point of its swing it collides with a piece of modern sculpture Since the sculpture is made of wet clay it sticks to the wrecking ball The wrecking ball has mass 200 kg The sculpture has mass 100 kg DIGIT 10 A m 3 H held in place A by crane sculpture During the collision A kinetic energy of whole system remains constant B linear momentum of whole system remains constant C angular momentum of ball about point of suspension A remains constant D impulse on the sculpture is zero Maximum height reached by system ball sculpture on the right side is B 3m 20 C m 9 D 5 m

c 2 cm d 25 A particle having initial velocity 10 m s moves with a constant acceleration 5ms 2 for a time 15 second along a straight line what is the displacement of the particle in the last 2 second a 17 5 m c 21 m b 20 m d 23 m

7 Let P Q and R represent the positions of the car at different instants of time O P R Q 160 120 80 40 0 40 80 120 160 200 240 280 320 360 400 X axis Consider the following statements with reference to the above situation I Distance moved by the car from O to P is OP 360m II Distance and path length are same so path length traversed from O to P is also OP 360 m III If the car moves from O to P and then moves back from P to Q the path length traversed is OP PQ 480 m IV If the car moves from O to P and then moves back from P to Q the path length traversed is OQ 240 m Choose the correct option a Statements I II and III are correct b Statements I II and IV are correct c Statements I and III are correct

28 A juggler maintains four balls in motion making each of them to rise of height of 40m from his hand what time interval should be maintain for the proper distance between them a 1 71 seconds c 1 41 seconds 9 A ball is thrown vertically un b 2 14 seconds d 4 seconds

16 An athlete participates in a race now he is moving on a circular track of radius 80 m completes half a revolution in 20s Its average velocity is a 8 m s b 16 m s c 10 m s d 12 m s motion of a particle is described by the equation 17 The

d None of these 14 A truck travels a distance A to B at a speed of 40 km h and returns to A at a speed of 50 km h then what is the average velocity of the whole journey a 34 5 km h b Zero c 35 km hr d 40 km hr

2 A particle moves for 50 seconds if first accelerates from rest and then retard or deaccelerates to rest If the retardation be 5 times the acceleration then the time for retardation is a 25 3 second c 25 second b 50 3 second d 100 3 second

A ball is projected with speed 20 2 ms at an angle of 45 above the horizontal The angular velocity of the ball when it is at its highest point of journey about point of projection is 1 0 4 rad s 2 0 3 rad s

c 50 m s d 55 m s 42 Water drops falls at regular intervals from a tap which is 8 m above the ground The third drop is leaving the tap at the instant the first drop touches the ground the second drop at that instant is at height a 2 m b 6 m c 4 m d 6 05 m A shuttle cork bitt JC

59 The position of an object moving along X axis is given by x a bt where a 8 5 m b 2 5 ms 2 and t is measured in seconds C For the above situation match the terms in Column I with the values of Column II and choose the correct option from the codes given below Column I A Velocity of object at t 2 0 s B Velocity of object at t Os C Instantaneous speed of object at t 2 0 s a A 1 b A 2 A 4 A 3 d D Average velocity between t 2 0 4 10 ms s and t 4 0 s Codes B 2 B 3 B 3 D 2 Column II C 3 D 4 C 4 D 1 C 2 D 1 1 15 ms 10 ms 2 3 0 ms Cho a C 61 TH of a b 62 C

9 A particle is moving along x axis Its position varies with time as x 37 27t where x is in metre and it is in seconds The distance of particle from origin O when it comes to rest is 1 65 m 2 78 m 3 91 m 27m

52 The acceleration a of the body starting from rest varies with time following the equation a 8t 5 The velocity of the body at time t 2 sec will be a 22 m s b 26 m s c 28 m s d 30 m s

Two masses A and B having mass m and 2m respectively are kept on a smooth horizontal table as shown in the figure B is given a velocity v perpendicular to the string parallel to the table The tension in string is T 2my nl Value of n is A l

21 A block of mass 4 kg is kept over a rough horizontal surface The coefficient of friction between the block and the surface is 0 1 At t 0 31 velocity is m S imparted to the block and simultaneously 21 N force starts acting on it Its displacement in m in first 5 s is a 8 b 81 c 3

A particle falls from rest under gravity from a height H and hits an inclined plane After collision the velocity becomes horizontal without changing the speed The maximum horizontal distance covered by the particle will be H Fixed H 1 2 tan 0 cos 0 H 2 tan 0

A horizontal insulated cylinder of volume V is divided into four identical compartments by stationary semipermeable thin partitions as shown in figure The four compartments from left are initially filled with 28 g helium 160 g oxygen 28 g nitrogen and 20 g hydrogen respectively The left partition lets through hydrogen nitrogen and helium while the right partition lets through hydrogen only The middle partition lets through hydrogen and nitrogen both The temperature T inside the entire cylinder is maintained constant After the system settles into an equilibrium He 0 11RT V Pressure of helium is Pressure of oxygen is Pressure of nitrogen is Pressure of hydrogen is 19RT V 4RT V 10RT V N H

0 A particle is moving in the X Y plane At t 0 it is located at the origin O 0 0 and its velocity is v0 b 32 3 where b is a positive constant and 2 3 are unit vectors in the positive x and positive y directions Its acceleration is constant and given by a 2 3 In its subsequent motion t 0 it will cross the x axis at the instant of time given by Ot b Ot 3b Ot 2b t 4b L

A particle starts moving rectilinearly at time t 0 such that its velocity v changes with time 1 as per equation v t 2t m s for 0 t 2 s 1 6t 8 m s for 2 t 4 s a Find the interval of time between t 0 and t 4s when particle is retarding b Find the maximum speed of the particle in the interval 0 t 4 s

15 Two bikes A and B are moving in the same direction with velocities u and u uu When the bike A is at a distance s behind the bike B the driver of the bike A applies breaks producing a uniform retardation a There collision in the two bikes is avoided only when a s u u 4B 2a b s U U 2a only

Which of the following statements is incorrect regarding motion of particle along straight line v t graph is a straight line inclined to time axis for uniform acceleration x t graph is parabola if motion is uniformly accelerated x t graph is a straight line inclined to time axis if motion is uniform and acceleration is zero v t graph is parabola if motion is uniformly accelerated

In the situation shown reading of the spring balance will be F 15 N 2 kg 0 5 3 kg 0 5 2 33 N 4 40 N F 60 N 1 30 N 3 36 N Time period of a conical pendulum of length 20 cm

A stone is projected from the ground with velocity 50 m sec at an angle of 30 If crosses a wall after 3 second How far beyond the wall the stone will strike the ground g 10 m s Question Type Single Correct Type 1 90 2 m 2 89 6 m 3 86 6 m

30 m From the point on the ground at a distance 30 m from the foot of a pole a ball is thrown at an angle of 450 which just touches the top of the pole and lands further 60 m from the foot of the pole on other side height of the pole is 45 m 22 5m Physics Single select 20 m Physi A 27

d The motion has no turning points 4 A vehicle travels half the distance with speed v and the other half with speed v then its average speed is b 2v V V V a C V V 2 2v V V V d V V V V 10

A ball is thrown up with an initial velocity V Air friction acts on it against its direction of velocity If it takes time ta to reach the top and time to to fall down Then O t tg t t ch

A projectile has the maximum range of 100 3 m If the projectile now thrown up along a smooth inclined plane of angle of inclination 60 with same speed the maximum displacement covered by it along the inclined will be 80 m 150 m 100 m 50 3 m