Kinematics Questions and Answers

A boy sees a ball going up and then back down through a window 2 45m high total time the ball is in sight for up and down motion is 1 sec The height abou window that the ball rises is 1 0 98 m 2 0 49 m 3 0 245 m 4 0 306 m

At t 0 a stone of mass 10 g is thrown straight up from the ground level with a speed 10 m s After 1 s a second stone of the same mass is thrown from the same position with a speed 20 m s What is the position of the first stone from the ground level at that moment Take g 10 m s 1 10 m 2 1 m 3 2 m 4 5 m

31 A capillary tube is dipped in water to a depth and the water rises to a height h 0 in the capillary tube The lower end of the tube is closed in water by putting a thumb over it The tube is now taken out and the thumb is removed from the lower end and it is kept open The length of liquid column in the tube will be a c h h b l h d 2h

TRIANGLE MOTION OF BALL ON INCLINED PLANE A particle is released from the top of an equilateral triangular groove which lies in the plane of an incline plane of inclination 0 53 as shown in figure The corners of triangular groove are curved to neglect impulse Side of triangle is 8 3m Calculate the time of a complete round trip after releasing the ball from top At corners of triangle due to curve ignore any change in speed of ball 9 a 6 830 4 x 1 2 4 3 m s 1 853m t 2 2 1 2l 2x8 3 23 a a gris3 48 vel at bottom of grove v 9 4 3x2 853m 853 18 8 3 53

A hypothetical spherical planet of radius R and its density varies as p Kr where K is constant and r is the distance from the center Determine the pressure caused by gravitational pull inside r R the planet at a distance r measured from its center

n the arrangement shown the blocks have masses m and m the pring constant is k and coefficient of friction is u Initially the lower lock is held at rest keeping the spring relaxed and the vertical and horizontal segments of the cord straight Find maximum possible speeds of the blocks after the lower block is released www my

1 A student tries to raise a chain consisting of three identical links Each link has a mass of 300 g The three piece chain is connected to a string and then suspended vertically with the student holding the upper end of the string and pulling upward Because of the student s pull an upward force of 12 N is applied to the chain by the string a Draw a free body diagram for each of the links in the chain and also for the entire chain considered as a single body

The position of an object at any time t is given by s t 3t 4 40t 3 126t 2 9 a Determine the velocity of the object at any time t b Does the object ever stop changing c When is the object moving to the right and when is the object moving to the left

Illustration 1 A body moves 6 m north 8 m east and 10 m vertically upwards what is the magnitude of the resultant displacement from initial position

betwee A spring is compressed two toy cars of masses M an M When the cars are release they move apart If X and X b the displacements of the cars whe in contact with the spring then A M x1 M x2 M x2 M x1 B M x M x O M x M x D C

21 Raindrops are falling vertically with a velocity 10 m s To a cyclist moving on a straight road the rain drops appear to be coming with a velocity of 20 m s The velocity of the cyclist is 1 10 m s 3 20 m s 2 10 3 m s 4 20 2 m s www m SUURE

A projectile is projected at some angle from the ground towards east in the absence of air resistance then time period and range of projectile are T and R If wind starts blowing towards east with some acceleration then the new time period T and range R have the relations 1 T T and R R 2 T T and R R 4 T T and R R T and R S

13 Preeti reached the metro station and found that the escalator was not working She walked up the stationary escalator in time t On other days if she remains stationary on the moving escalator then the escalator takes her up in time t2 The time taken by her to walk up on the moving escalator will be 1 1 d t 1 NEET 2017 t t a 1 1 2 b c t t2 t 1

A particle is projected with velocity v along x axis The deceleration on the particle is proportional to the square of the distance from the origin i e a x The distance at which particle stops is 1 2 1 3 3 3 4

Consider collision of two billiard balls with equal masses m m2 First ball is targeting and second is target Target was at rest and targeting ball hits at target with speed of 30 m s and gets deflected from initial direction through an angle of 37 What is speed of second ball after collision 1 16 m s 2 18 m s 3 20 m s 4 8 9 m s

The acceleration of a particle starting from rest varies with time according to the relation a kt c where k and c are positive constant The velocity o the particle after time t will be 1 kt ct 3 kt c 2 1 2 kt ct 2 1 4 kt ct 2

5 The kinetic energy acquired by a mass m in trav certain distance d starting from rest under the action of a force F such that the force F is directly proportional to t is a Directly proportional to 12 b Independent of t c Directly proportional to t ortional to t

4 Boating A boat is traveling in a river with a current that has a speed of 1 5 km h In one hour the boat can travel twice the distance downstream as it can travel upstream What is the boat s speed in still water

Q3 Variation of acceleration of a particle moving along a straight line is given by a 2sint m s If initial velocity of the particle is 1 m s its maximum velocity IS a m s 1 3 55 m s 3 4 57 m s t s 2 2 55 m s 4 3 14 m s

9 ons The velocity displacement graph of a particle is shown in the figure V xo The acceleration displacement graph of the same particle is represented by 1 2 3 4 a a X a x X

Q176 A balloon is moving upwards with velocity 9 8 m sec It releases a stone which comes down to the ground in 11 sec The height of the balloon from the ground at the moment when the stone was dropped is a 492 9 m b 490 m c 485 1 m correct d 494 5 m

PQ is a smooth inclined plane whose angle of inclination can be varied in such a way that point Q remains fixed P can move on a vertical line PR A particle slides from rest from point P At different values of 0 time for descent t from P to Q is noted The following statement is true about t A minimum value of t is 2 B t is minimum when 8 approaches 90 C to decreases continuously as 8 is increased D t first increases then decreases as 0 is increased A particle at a height h from the ground is projected with an angle 30 from the borontal ground making angles 45 wil

A body is dropped from a height of 100 m At what height the velocity of the body will be equal one half of velocity when it hits the ground A 45 m B 55 m C 65 m D 75 m A window is

8 A car is moving on a straight road with uniform acceleration The speed of car varies with time as follows Speed m s 5 10 15 20 25 30 Time s 0 10 20 30 40 50 Calculate a The acceleration of car b Distance travelled by the car in 10 seconds 3

37 A stick AB of length 1 stands vertically on a horizontal floor leaning on a wall A beetle P starts climbing the stick from the floor When the beetle starts climbing the lower end B of the stick is made to move away from the wall with a constant velocity u The beetle climbs the stick with a constant speed u relative to the stick If the upper end A does not leave the wall what maximum height can the beetle rise

A boat takes 2 hours to travel 8km and back in still water If velocity of river is 4 km h the time taken for going 8 km upstream and coming back is 1 2h 2 2h 40 min 3 1h 20 min 4 Not possible

A hot air balloon is rising straight up with a speed of 3 0 m s A ballast bag is released from rest relative to the balloon at 10 8 m above the ground g 10 m s Time elapses before the bag hits the ground is 1 8 s The maximum height reached by bag from the ground is 11 25 m The time when the bag reaches its maximum height is 0 3 s The height of balloon from ground when the bag hits the ground is 16 2 m

A helicopter flying horizontally with a constant velocity of 180 km hr drops a box above a point A on an inclined plane The box lands 10 seconds later at a point B on the inclined surface The value of d 4h is where h and d are in meter g 10 25 m s h A d p 180 km hr B 37

A projectile takes off with an initial velocity of 50 m s at an angle of 37 with horizontal It is just able to clear two hurdles of height 25 m each separated from each other by a distance d Calculate d in m g 10 m s

A snowmobile is originally at the point with position vector 29 3 m at 95 0 counterclockwise from the x axis moving with velocity 4 17 m s at 40 0 It moves with constant acceleration 1 91 m s at 200 After 5 00 s have elapsed find the following a its velocity vector v m s b its position vector m

A force F 0 5x 10 acts on a particle Here F is in newton and x is in metre Calculate the work done by the force during the displacement of the particle from x 0 to x 2 metre

36 Please answer the below given question A particle is projected from horizontal surface of earth at speed u making an angle 0 COS 1 15 72 the horizontal If equation of trajectory for the particle is y kx 2x where k is a constant then wha the speed in m s of projection Assume that particle was projected from origin and motion of particle is xy plane where x axis is along the horizontal direction and y axis is vertically upward Take g 10 m s

33 A 10 kg boy standing in a 40 kg boat floating on water is 20 m away from the shore of the river If the boy moves 8 m on the boat towards the shore then how far is he from the shore Assume no friction between boat and water a 12 0 m 13 6 m c 12 8 m 11 6 m b d projected up a speed of 10 after I s is a 10 m s c 0 40 In the above

107 A ball is thrown vertically upwards with velocity 600 m s Calculate distance travelled in last 2 sec of its upward motion 1 20 m 3 10 m 2 30 m 4 25 m

A block is projected along a rough horizontal road with a speed of 10 m s If the coefficient of kinetic friction is 0 10 how far will it travel before coming to rest

Consider a vehicle going on a horizontal road towards east Neglect any force by the air The frictional forces on the vehicle by the road a is towards east if the vehicle is accelerating b is zero if the vehicle is moving with a uniform velocity c must be towards east d must be towards west

2 200 cal minute heat energy is supplied to a solid of 100 g The temperature of solid Q varies with time as shown The latent heat of fusion of the substance is Q 0 C Q 0 0 5 1 6 cal g 3 24 cal g 20 30 40 Minute 2 18 cal g 4 30 cal g

A heavy stone is thrown from a cliff of height h with a speed v The stone will hit the ground with maximum speed if it is thrown a vertically downward b vertically upward c horizontally d the speed does not depend on the initial direction

Two balls are dropped from same height at 1 second interval of time The separation between the two balls after 4 second of the drop of the 1s ball is a 30 m c 40 m b 35 m d 48 m

An potential energy curve U x is shown in the figure What value must the mechanical energy Emec of the particle not exceed if the particle is to be trapped within the region shown in graph A 3 J B 5 J C 6 J D 8 J r x n 8 10 AB CDEF GH X

A disc is rotating with constant angular velocity When a constant torque of magnitude 14 22 Nm is applied the disc stops rotating after completing 10 rotations the change in the kinetic energy of the disc is A B AKHI 100 J 20 J 80 J

projectile is launched from a point on a horizontal plane with a speed 10 2 m s making an angle 60 with the horizontal The interval of time between two instants when the kinetic energy of projectile is equal to its potential energy is Take reference as the horizontal level g 10 m s 1 1 s 2 2 s LO

4 Figure shows a graph of acceleration of a particle moving on the x axis Plot the following graphs if the p is at origin and at rest at t 0 velocity time graph ii displacement time graph iii distance time graph 2m s 2m s 5 10 15 20 25 30 35 40

1 The position coordinates of a projectile projected from ground on a certain planet with no atmosphere are given by y 4t 2t m and x 31 metre where t is in second and point of projection is taken as origin The angle of projection of projectile with vertical is 1 30 3 45 2 37 4 60 27

20 96 x 9 81 N 205 N Example 4 6 A 0 050 kg bullet travelling with an initial velocity of 400 m s penetrates into a wall with an average force of 4 x 104 Newton It goes out of the wall with a velocity 50 m s What is the thickness of the wall Another bullet of lower mass but travelling with the same velocity and exerting the same force cannot go out of the wall J EE 91 What is its maximum mass ton s third low the resisting force acting on the bullet P 4 x 104 N

4 The position x of a particle moving in a straight line along x axis varies with time t as t x 3 where x is in metres and t is in seconds The displacement of particle till it comes to rest is 1 9 m 2 5 m

A particle having a velocity v vo at t 0 if decelerated at a rate equals to B v where is positive constant After what time and after covering what distance will the particle come to rest a 213 2 2 1 2 0 B 3 B 3 2 11 23 vo Vo 0 6 d 1 2 2 9 B 3 B 3 2 Vo 0 3 2 0 5 2 5 vo Vo F

Find acceleration of block along inclined plane acceleration due to gravity g 10 ms smooth 37 m

12 A person holding a rifle mass of person and rifle together is 100 kg stands on a smooth surface and fires 10 shots horizontally in 5 s Each bullet has a mass of 10 g with a muzzle velocity of 800 ms The final velocity acquired by the person and the average force exerted on the person are a 0 08 ms 16N b 0 8 ms 8 N c 1 6 ms 16 N d 1 6 ms 8 N

c a spinning cricket ball that turns sharply on hitting the ground d a tumbling beaker that has slipped off the edge of a table The position time x t graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig 3 19 Choose the correct entries in the brackets below a A B lives closer to the school than B A b A B starts from the school earlier than B A c A B walks faster than B A d A and B reach home at the same different time e A B overtakes B A on the road once twice