Kinematics Questions and Answers

A uniform slender bar AB of mass m and length I supported by a frictionless picot at A is released from rest at its vertical position as shown in the figure If the reaction at pivot when the bar just acquires the horizontal position shown c 4 dotted is mg find the value of c B I

A grasshopper sits in an open rectangular box which can jump with an initial speed v 3 m s at any angle to the horizon What is the minimum angle a to the horizon to tilt the box so that the grasshopper can jump out of it Think that each side of the box is a square with a side h 52 cm The acceleration of gravity is g 10 m s Neglect air resistance g h h

5 3 For a particle moving on a circle of radius 18 m the distance covered s as a function of time t is given as s 3t2 s is in metre and t is in second The acceleration of the particle at t 2 second is 6 m s 2 8 m s 3 10 m s2 4 14 m s G 2 43

A starts from rest and moves with acceleration a Two seconds later B starts from rest and moves with an acceleration a2 If the displacement of A in the 5th second is the same as that of B in the same interval the ratio of a to a2 is

A train covers a distance of 4 km between two cons tions in 4 min If the acceleration of the train in the first part of the path is a and the retardation in the second part is 42 then show that 1 1 4 min km a1 az

A boy runs on a circular track of radius R in km with the speed of km h in the clockwise sense for 3 h and then with TR km h in the anticlockwise sense for 1 h The magnitude of his displacement will be 1 TR 2 E 4 R 2 3 37R 2 VER

Good morning students science homework 1 Determine the velocity of a train in km hour units after 20s when it is moving on a straight track with a uniform acceleration of 1 5m s2 after starting from rest 2 A scooterist travelling with a velocity of 20 km h accelerates with an acceleration of 0 10 m s 2 After what time will its velocity be 38 km h 10 17 ar

A bar AB and a block P are placed on a frictionless horizontal floor with their adjacent vertical faces in contact as shown in the figure by a top view Here the x y plane of a co ordinate frame is in the plane of the floor The bar is made to move horizontally along the floor in a straight line with a constant acceleration without rotation Direction of motion of the bar makes an angle sin 0 6 with the positive x axis Coefficient of friction between the block and the bar is 0 75 The distance travelled by the block until the plank moves a distance L 40 cm is C C A B 30 cm P 1 Lox X B C 1 5 cm D 0 15 cm

Two plates AB and CD are rigidly attached perpendicular to the base of a massive box The box is released on a smooth inclined plane having angle of inclination 37 With what minimum speed with respect to box should a particle be projected so as to graze top points A and C of the two plates AB 2m CD 3m Separation between top of plate is 3m Take g 10 m s Smooth

Paragraph for Q No 14 and 15 A projectile is fired from the height H and with velocity v making angle 0 with the horizontal H R 4 The angle 0 at which the range R is maximum is 1 tan 1 V 2gH 3 tan V 2v 2gH 15 The maximum value of range R is 1 2v 2gH 2 tan 1 2v gH 4 tan V 2 v gl V 2v v 4 v gH 2gH

A particle moving in one dimension with a constant acceleration of 2m s2 is observed to cover a distance of 5m during a particular interval of 1s The distance covered by the particle in the next 1s interval is in metre

Ball is rolled in a straight line with a speed of 5 ms1 towards a wall lying 20 m away After collision with wall ball retraces the path with a speed of 4 ms 1 What is the average velocity of ball during the time interval 0 to 6 sec A zero B 2 ms 1 C 4 ms 1 D 5 ms 1

any time The velocity of a certain particle moving along the x axis is proportional to x At time t 0 the particle is located at x 2 m and at time 10 s it is at x 4 m What is the position at t 5 s

e vertical diameter of a circle in a vertical plane Another diameter CD makes an angle of 60 with AB e ratio of the time taken by a particle to slide along AB to the time taken by it to slide along CD is I B 2 1 C 31 4 21 2 D 1 2

The motion of a body is given by the equation dv t dt 6 0 3v t where v t is the speed in m s and t is time in second If the body was at rest at t 0 1 the terminal speed is 2 0m s 2 the magnitude of the initial acceleration is 6 0m s 2 3 the speed varies with time as v t 2 1 e t m s 4 the speed is 1 0 m s when the acceleration is half the initial value

20 A lift is going up The variation in the speed of the lift is as given in the graph What is height to which the lift takes the passenger A 3 6 m B 28 8 m C 36 0 m Velocity m sec 3 6 Time sect 10 12

The friction coefficient between the horizontal surface and each of the block shown in the figure is 0 2 The collision between the blocks is perfectly elastic Find the separation in cm between then when they come to rest Take g 10 m s 1 0 m s 2 kg 16 cm 4 kg

A small block is released on the top of a wedge that is placed on a horizontal floor as shown in the figure Mass of wedge is M and angle of inclination of its start face is 0 Friction between wedge and floor is sufficient to prevent sliding and coefficient of friction between the wedge and the block is The mass of the block be so that the wedge will not topple m A 0 m if p 2 tang M 3sin 0 sin 8 ucos if tano M B 0 m if p tane M D m 3 sin 0 cos0 if a tane

A lift A is accelerating vertically upwards with acceleration 5 m s and another lift is accelerating downwards with acceleration 5 m s A coin is released from rest with respect to lift from some height in lift A At that instant velocity of lift A is 8 m s vertically upwards velocity of lift B is 12 m s vertically downwards Then velocity acceleration of coin with respect to lift B at that instant will be respectively Question Type Single Correct Type 1 2 4 m s 15 m s 3 20 m s 20 m s 4 4 m s 16 m s 20 m s 5 m s

Zero Marks 1 0 If none of the option is selected Negative Marks 1 If wrong option is selected A massive ball is falling down from an initial height of h 20 m With a gun held horizontally d 50 m far from the trajectory of the falling ball at the height of h 10 m we are going to shoot at the falling ball The bullet leaves the gun at a spee of v 100 m s At what time after the start of the fall should the gun be fired in order to hit the falling ball with the bullet The air resistance is negligible 0 75 O 1 00 s O1 32 s 1 715

The displacement of a body from reference point is given by x 2t 3 where x is in meter and t in seconds This shows that A the body is at rest at t 3 2 sec B the body is speeding up at all times C the body is decelerated from t 0 to t 3 2 sec D the distance travelled by body in 2 sec is 10 m

La ao 2 An aeroplane is flying from cityA to city B along path 1 The path 1 is a circular arc whose centre coincides with the centre of the earth Another aeroplane is flying along path 2 from A to B The path 2 is circular arc whose centre is at C O is the centre of the earth A 2 C 3 A particle is moving on a circular path of radius R with constant 0 B Then a The distance travelled by 1st aeroplane is greater than that of 2nd aeroplane b The distance travelled by 1st aeroplane is less than that of 2nd aeroplane The displacement of both aeroplane is different d None of these c

46 A body initially at rest starts moving along x axis in such a way so that its acceleration verses displacement plot is as shown in figure The maximum velocity of particle is A 1 m s B 2 m s C 6 m s D 4 m s

1 A point moves in a straight linen so that distance from the start in time t is equa 1 4 14 41 161 10 A At what times was the point at its start position 85 0 4 85 B At what times is its velocit

49 The velocity v and displacement x of a particle executing simple harmonic motion are related dv dx as v w x At x 0 y v The velocity v when the displacement becomes x w x B v A v v w x 2 C v v B v v w x 0 D v v w x2 0

16 Velocity of a particle varies as v 2t 3t in km hr If t 0 is taken at 12 00 noon a Find the expression for the acceleration of the particle b Find the time between 12 00 noon and 1 00 pm at which speed is maximum c What is the time at which speed of the particle is minimum d What is the velocity of the particle is 12 00 noon

48 Two bodies move from the same point along a straight line The first body moves with velocity v 31 61 m s the second with velocity v 101 20 m s At what instant and at what distance from the initial point will they meet A 10 s 700 m C 30 s 700 m B 20 s 500 m D 40 s 500 m

31 A projectile is given an initial velocity of 1 31 m s where i is along the ground and jis along the vertical Then the equation of the path of projectile is Take g 10 m s a y 3x 5x C X V3 y 5x2 b y 3x 5x d x y 3

Velocity equal to zero 2 A particle moves in a straight line according in the law x 4a 1 a sin where x is 11 position in meters t in sec a is so constants then the velocity is zero at 12 The velocity o

36 Figure shows the position of particle moving along x axis as a function of time Which of the following statement is correct x m 20 10 D 0 2 B 4 6 t s 1 The particle has come to rest 3 times 2 The maximum speed is at C 3 The average velocity for total period shown is positive 4 Velocity remains positive for first 4 second of motion Il ir proiected is taken as 41 A

A mass of 1 kg is acted upon by a single force F The mass is displaced from 0 0 to 1m 1m If initially the speed of the particle was 2 m s along the direction of displacement its final speed should approximately be 0 5n m s Find n report an integer O O O 1 4 4 N 3

A projectile has the maximum range 500 m If the projectile is thrown up a smooth inclined plane of 30 with the same magnitude velocity the distance covered by it along the inclined plane till it stops will be a 250 m b 500 m d 1000 m c 750 m

Example 4 A particle is projected with a velocity of 20 m s at an angle of 30 to an inclined plane of inclination 30 to the horizontal The particle hits the inclined plane at an angle of 30 during its journey Find the a time of impact b the height of the point of impact from the horizontal plane passing through the point of projection

A box is travelling with a speed of 6 7 m s when it coasts up a frictionless incline which is 45 degrees above the horizontal Determine the distance which the box will travel along the incline before coming briefly to rest

A particle starts with an initial velocity 2 5 m s along the positive x direction and it accelerates uniformly at the rate 0 50 m s a Find the distance travelled by it in the first two seconds b How much time does it take to reach the velocity 7 5 m s c How much distance will it cover in reaching the velocity 7 5 m s macarpe

A streamer going downstream overcomes a wooden log at a point P one hour later the streamer turns back and after sometime passes the wooden log at a distance 6 km from point P the speed of river is

Circle b Parabola d Hyperbola A particle starts with velocity u and moves with constan acceleration a What is the nature of graph between the time t and displacement x a Straight line Symmetric parabola c Asymmetric parabola d Rectangular hyperbola 5 A particle starts from rest and moves with constan 11 1

A sphere of radius 1 cm is thrown horizontally with a velocity of 30 m s G and angular velocity of 3000 rad s from the top a tower of height 20 01 m Assume coefficient of friction between ground and sphere to be 1 and coefficient of restitution to be zero What is the horizontal distance covered by C M of sphere before coming to rest Neglect air resistance A 45 m C 40 m B 20 m D none of these

stone remains in the air a 6 s b 5 s c 7 s d 4 s 326 Two identical metal spheres are released from the top of a tower after seconds of each other such that they fall along the same vertical line If air resistance is neglected then at any instant of time during their fall a the difference in their displacements remain the same b the difference between their speeds remains the same Jos e the difference between their heights above ground is to 1 proportional to d the difference between their displacements 332 A partic in a stra respecti 2 a c e 2 U 2

but the freely falling An elevator in which a man is standing is moving up with a speed of 10 m sec If the man drops a coin f height of 2 45 metre it reaches the floor of the elevar a time g 9 8 m sec

20 A bomb is projected at an angle 60 with the horizontal with a speed of 20 m s At the highest point of its trajectory it explodes into three parts of equal masses If just after explosion one part comes to rest and 2nd part retraces its path then the distance of third part from the point of projection when it strikes the ground is consider ground to ground projection 1 20 3m 3 40 3m 30 3m 150 m

A particle starts from rest and moves with accleration a 4sin m s where t is in nt seconds Initially the particle is at origin and moves along x axis then 16 1 Maximum speed of the particle is m s TC 2 Direction of acceleration changes alternatively 3 Direction of velocity changes alternatively 8 4 Speed of the particle is m s at t 1s

A man throws a packet from a tower directly aiming at his friend who is standing at a certain distance from the base which is same as the height of the tower If the packet is thrown with a speed of 4 m s and it hits the ground midway between the tower base his friend than the height of the tower is g 10 m s 5m 8 m C 3 2 m Correct Answer

4 120 28 A particle is projected with a velocity v such that its range 28 f K 4 211 tam o on the horizontal plane is twice the greatest height attained by it The range of the projectile is where g is acceleration due to gravity B 2 4 tan 0 tam o 4v 5g 1 4g 5v 9 A truck travelling dun part 2 K Ei 3 9 3 K Ef 4 f 21 4 4v 59 tamp 4 2 H 2 45 3 60 4 120 54 1 g 4v 5g V R 2M 4 ax 2 tan o Ftano 24 42 20 4g 5v 3 4v 4 50

23 Three ships A B C are in motion The motion of A as seen by B is with speed v towards north east The motion of B as seen by C is with speed v towards the north west Then as seen by A C will be moving towards 1 north 2 south 3 cast 4 west A man wishes to cross a river in a boat If he crosses the river in minimum time he takes 24

The radius of curvature of a planar trajectory can be defined as dy dx R x y dx Alternatively one can also define radius of curvature of a trajectory at a small interval around the poi p x y to be v a where v represents the tangential speed and a represents the normal component acceleration of the particle at the point P A certain particle moving in the xy plane has a trajectory who velocity at any point is defined as v al bxj a and b are positive constants At time t 0 the parti was located at the origin 28 The minimum radius of curvature is at A origin 2a b C 1 B b a a D infinity

11 Initially car A is 10 5 m ahead of car B Both start moving at time t 0 in the same direction along a straight line The velocity time graph of two cars is shown in figure The time when the car B will catch the car A will be Car B 10m s L Car A 1 1 t 21 sec 2 t 2 5 sec 3 20 sec 4 none 12 A car is moving with uniform velocity

S Problem 16 Fig 5 65 shows two identical capacitors C and C of 1uF capacitance connected to a 6 V battery Initially switch is closed After some time S is left open and dielectric slab of dielectric constant S inserted to fill completely the space between the plates of two 3 are capacitors How will i the charge and ii the potential difference between the plates of the capacitor be affected after the slabs are inserted CBSE 2011 Solution Initially when switch is closed For capacit 6V C 1 F Fig 5 65 C 1uF

er out of which ONE OR MORE is are correct king scheme 4 for correct answer 0 if not attempted and 1 in all other cases Find the forces in the hinged rods BC and AC if AB 60 cm AC 1 2 m BC 1 6 m see figure Hanging mass has a mass of 50 kg the mass of the rods can be neglected C is hinge V

In a photo cell 4 unit photo electric current is flowing the distance between source and cathode is 4 unit Now distance between source and cathode becomes 1 unit What will be photo electric current now