Kinematics Questions and Answers

A particle starts from rest and accelerates constantly with a m s2 for T second and then retards uniformly with same rate till it comes to rest The position time x t graph of the particle is best represented by NCERT Pg 45 1 3 X h T 2T X T 2T 2 4 T 2T X A T 2T

5 Two particles of equal masses moving with same speed collide perfectly inelastically After the collision the combined mass moves with half of the speed of the individual masses What is the angle in degree between the initial momenta of individual particle

13 A vertical hanging bar of length and mass m pe unit length carries a load of mass M at lower end its upper end is clamped to a rigid support The tensile stress a distance x from support is A area of cross section of bar 1 N 3 Mg mg 1 x A Mg mgl A 2 4 Mg A M m gx AL

ceship travelling away from Earth at 75 0 the speed of light fires a probe in a direction perpendicular to its motion at 80 0 the speed of ve to the spaceship What is the speed of the spaceprobe as measured as percentage of the speed of light

36 A particle of mass m is projected with velocity v making an angle of 45 with the horizontal The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is where g acceleration due to gravity 1 Zero 3 mv 2g 2 m 4 2g 4 mv 2g

Two parallel rail tracks run North South Train A moves North with a speed of 54 km hr and train B moves South with a speed of 90 km hr What is the velocity of B with respect to A in m s Choose the positive direction of x axis to be from south north O 40 0 O 55 0 O 30 0 450

An airliner passes over an airport at noon traveling 510 mi hr due east At 1 00 p m another airliner passes over the same airport at the same elevation traveling due north at 560 mi hr Assuming both airliners maintain their equal elevations how fast is the distance between them changing at 2 00 p m The equation relating the horizontal distance between the first airliner and the airport a the horizontal distance between the second airliner and the airport b and the horizontal distance between the two airliners c is a b c Differentiate both sides of the equation with respect to t 2a da 2b dt Do not simplify db dt 2c dc dt At 2 00 p m the distance between the airliners is changing at a rate of about Round to the nearest tenth as needed mi hr

A particle is projected from point A at an angle of 53 with horizontal At the same time wedge starts from rest and moves with constant acceleration a as shown The 4 value of a in m s2 for which the partide strikes incline perpendicular at Pis g 10 m 2 15 3 a P wedge 45 45 r 153 A

A concrete statue of a banana is hung from two ropes as shown below The right side rope has a tension of 230 Newtons What is the mass of the concrete banana Take the center of mass of the banana to be its horizontal midpoint 0 53 m 1 75 m 0 15 m

A spaceship travelling away from Earth at 75 0 the speed of light fires a spaceprobe forwards ie also away from Earth at 80 0 the speed of light relative to the spaceship What is the speed of the spaceprobe as measured from Earth as a percentage of the speed of light

particle is moving in the X Y plane Its position as a function of time is given by F cos 3r i 2 sin 3r Let t to be the first instant after t 0 when the force acting the particle is perpendicular to its velocity The distance of the particle from the origin att to is

5 In a system of particles 8 kg mass is subjected to a force of 16 N along ve x axis and another 8 kg mass is subjected to a force of 8 N along ve y axis The magnitude of acceleration of centre of mass and the angle made by it with x axis are given respectively by 5 1 ms 0 45 2 2 3 5 ms 2 0 tan 2 3 5 2 3 ms 2 0 tan 1 2 2 4 1 ms 2 0 tan 3

The radius of curvature for a projectile motion on horizontal ground is minimum when the instantaneous velocity vector makes an angle a with horizontal where a is 1 0 3 45 2 30 4 60

A ball is thrown upward from the top of a building with an initial velocity of 30 m sec The height of th building is unknown but high enough so that the ball is still in motion for the first 5 seconds Assum the acceleration due to gravity is 10 m sec 1 2pts Find the velocity of the ball as a function of time t 2 2pts When does the ball reach the highest point 3 2pts Find the displacement traveled by the ball during 0 I 5 4 4pts Find the total distance traveled by the ball during 0 t 5

Q 12 In a region of space a uniform electric field E uniform magnetic field B and uniform gravitational field gexist in mutually perpendicular direction A charged particl moving with uniform velocity in this region Once the particle leaves this region and and where there is only g its speed begins to decrease How long after leaving the first regi does the velocity of particle reach the minimum value

Two fixed frictionless inclined planes making an angle 30 and 60 with the vertical are shown in the figure Two blocks A and B are placed on the two planes What is the relative vertica acceleration of A with respect to B AIEEE 2010 4 144 1 60 1 4 9 ms 2 in horizontal direction 3 Zero 30 2 2 9 8 ms 4 4 9 ms in vertical direction in vertical direction

Question No 14 A particle is projected vertically from a point on the ground at 0 The particle crosses a point Patr 1s and again atr 4s The height in metres of the point P from the ground 15 g 10m s Answer

The acceleration a t of a particle moving on the X axis varies with time as a t 31 1 for 0 t 2 a t 4 5t 1 for 2 t 4 Atr 0 the particle at rest atx 0 Which of these options is are correct The velocity of the particle at 1 i r 1is The displacement of the particle between 1 and 3 is 6 66 The velocity of the particle at 3 is The position of the particle at 4 isx 13 33

The acceleration a r of a particle moving on the X axis varies with time as a t 31 1 for 0 1 2 a t 4 51 1 for 2 1 4 Atr 0 the particle is at rest atx 0 Which of these options is are correct 7 The velocity of the particle at 1 is 6 The displacement of the particle between 1 and 3 is 6 66 13 The velocity of the particle att 3 is 2 The position of the particle at 4 is x 13 33

A particle of mass 1 kg is moving with constant velocity 20 m s along a straight line At t 0 a force F t At starts acting on the particle where t is time in seconds Fis in Newton and A 2 0 N s The direction of the force is always perpendicular to the velocity of the particle If the velocity of the particle at t 0 and at t 5 sis and respectively the angle in radians between and vis

A car starts from rest again comes to rest after traveling 200 m in a straight line If its acceleration and deacceleration are limited to 10 m s 20 m s respectively then minimum time the car will take to travel the distance is 1 20 s 2 10 s 3 2 15 s 4 20

Question No 17 A particle of mass 1 kg is moving with constant velocity 20 m s along a straight line Atr 0 a force F t Ar starts acting on the particle where t is time in seconds Fis in Newton and 4 2 0 N s The direction of the force is always perpendicular to the velocity of the particle If the velocity of the particle at 0 and att 5 s is and respectively the angle in radians between and vis Answer Enter your answer here

A particle moves on the curvey 4 at a constant speed 4 2 m s with x and y being in metres At the instant the X coordinate of the particle is 4 m its Y component of velocity in m s is

A body of mass kg is moved slowly from ground to the top of a hill of height h 10 m Force F is always tangential to the surface If 0 2 then find total work done by force F in joule g 10 m s F 20 m h 10 m

7 A sound wave of frequency n travels horizontally to the right with speed c It is reflected from a broad wall moving to the left with speed v The number of beats heard by a stationary observer to the left of the wall is Ans C D Observer 2ny Wall

The acceleration of a particle which moves along the positive x axis varies with its position as shown If the velocity of the particle is 0 8 m s at x 0 the velocity of the particle at x 1 4 is in m s A 1 6 B 1 2 0 4 0 2 a in m s 0 4 0 8 1 4 x in m C 1 4 D none of these

12 A 1500 kg car moving north collides with a 1000 kg car moving west After the collision the cars stuck together at more at an angle of 45 north or west at speed of 10 m s What is the initial speed of the 1500 kg a 11 8 m s b 14 m s c 20 m s d 10 2 m s e 18 m s

The velocity of a particle moving along x axis varies with its distance from origin as v k x Assuming that the particle starts from origin the position of the particle at any instant t is given by 1 x kt 2 x k t k 4 3 k 42 4

Fill in the Blank Options What is the acceleration of the block in the given diagram in m s 50 N 45 N 5 kg

Which of the following is true when a body is stationary O O The body is in vacuum O The force acting on it is not in contact with it O There is no force acting on it The combination of forces acting on it balance each other

A man is standing on a moving conveyor belt with his luggage adjacent to hir kept on the belt The belt is moving with velocity VB 0 5 m s When the man is a distance 20 m from end Q he starts walking at a velocity 1 5 m s relative to belt towards Q leaving his luggage there He walks upto Q and comes bac to his luggage walking back at same speed relative to belt P B conveyor belt 20m Time taken by man to reach end Q is 10 s Time taken by man to reach end Q is 20 s Time taken by man to return back to luggage is 20 s The separation of luggage from O when man returns back to luggage

A man riding a dirt bike made a jump from one cliff to another The cliffs are the same height and located 60 feet apart If he made the jump at an angle of elevation of 20 and cleared the jump by 10 feet in 1 2 seconds find his initial velocity A 44 93 ft s B 50 39 ft s C 55 72 ft s D 62 08 ft s E 65 19 ft s

9 In one dimensional motion instantaneous speed v satisfies 0 v vo malappA yaibola basq2 a The displacement in time T must always take non negative values b The displacement x in time T satisfies vo T x vT c The acceleration is always a non negative number d The motion has no turning points

A car starts from rest and moves with uniform acceleration a on a straight road from time t 0 to t T After that constant deceleration brings it to rest In this process the average speed of the car is aT 1 3 4 aT 2 2 3aT 2 4 aT

A body of mass 2 the top of a hill of height h 10 m Force F is always tangential to the surface If 0 2 then find total work done by force F in joule g 10 m s F kg is moved slowly from ground to 1 20 m h 10 m

A train appears to move at velocity 12 7 m s towards North West to a cyclist moving at a velocity 4 m s towards North Assumi ng that the speed of the cyclist and the actual velocity of the train both magnitude and direction remain unchanged througho ut which of these options is are correct The train s actual velocity is 20 m s in a direction tan West of North If the cyclist mov es towards East the train still appears to move towards North West to him If the cyclist moves towards East the train appear s to move at velocity 16v2 m s to him The velocity of the train as seen by the cyclist is maximum if he moves opposite to the dir ection of the train s actual velocity

A man throws a ball making an angle 60 with horizontal He runs on a level ground and catches the ball If he has thrown the ball with speed v Then avg velocity of the ball must be V

85 A rightward moving wave y x t A sin kx t 0 has initial condition y 0 at x 0 and t 0 Find the value of x and t at p 1 2 n for which particle acceleration will have the same value as for initial condition and 2n1 1 0 2 If and off are wordingth frequency Ans can be 2 f A 21

4 245 m 42 If is found that A B A This necessarily ir 1 B 0 A B 2AB 2 A and B are antiparallel 2 A 2A 3 A and B are perpendicular 4 A B 0

27 A particle is projected from the ground towards a fixed vertical wall with an initial velocity 15 m s The foot of the wall is at a distance 15 m from the point of projection It is desired that the particle hits a point P on the wall at a height 5 m from the ground It is observed that this can be achieved with two different angles of projection and If the time taken by the projectile to hit the point P when projected at angles and is and respectively and then g 10m s Choose 1 U 14 0 45 0 4 2 s 5 s t tan 15 m 2 4 5 m

A particle is projected from the ground towards a fixed vertical wall with an initial velocity 15 m s The foot of the wall is at a distance 15 m from the point of projection It is desired that the particle hits a point Pon the wall at a height 5 m from the ground It is observed that this can be achieved with two different angles of projection 0 and 0 If the time taken by the projectile to hit the point P when projected at angles 0 and 0 is and respectively and then g 10 m s 2 8 45 08 tan 2 4 2 s 0 12 5 s 15 m O 5m

A particle of mass m is projected with velocity Vo at angle 0 45 with horizontal The angular momentum of particle at its topmost position about point of projection is O mv 2g mV3 2 2g mv 4 2g C

A train of 150 metre length is going towards north direction at a speed of 10 m s A parrot flies at the speed of 5 m s towards south direction parallel to the railway track The time taken by the parrot to cross the train is 1998 A 7 s C 9 sald B D 8 s 10 s

A boat is moving with velocity 47 6 m s with respect to ground The water in the river is moving with 31 4 m s with respect to ground The velocity of boat with respect to water is 7 10 m s 1 2 m s 51 7 m s head More 57 8j m s

A shell is fired vertically upward with a speed of 60 m s When it is at maximum height it explodes into large number of fragments Assume that the fragments fly in every possible direction and all of them have same initial speed of 25 m s The minimum time taken in sec by any one fragment to reach at ground will be

The range of a projectile when launched at angle 20 is R When launched at angle 30 the range is still R Then value of e should be speed of projection in both case is same O 30 60 24 18 Clear

A car travelling at constant velocity passes a stationary motor cycle at a traffic light As the car overtakes the motorcycle the motorcycle accelerates uniformly from rest The following displacement time graph represents the motions of both vehicles from the traffic light onwards x m 375 300 5 x 10 motorcycle car 15 t s no intonal s speed of the motorcycle may be less than the speed of the car

V X y coordinates is given for a particle moving in x y plane from point A to point B Which of the following option s are incorrect ya A B X This graph represents path of the particle Particle does not change it s direction during the motion Average velocity from A to B is zero

A river is flowing at 2 m s A car starts from point B and travels along the bank of straight river towards right with velocity 8 m s At the same time a boat starts from point A directly opposite to point B to cross the river along a straight line such that moving with a speed of 10 m s in still water it catches the car on other bank Find how much time after starting the motion the two will meet B 200 m 2 m s

A graph between x y coordinates is given for a particle moving in x y plane from point A to point B Which of the following option s are incorrect YA This graph represents path of the particle A Particle does not change it s direction during the motion Average velocity from A to B is zero Particle travels in a straight line B X