Kinematics Questions and Answers

9 X Three vectors are shown in the figure below OA 1 unit OB 4 unit and OC 3 unit The sum of Y components of these vectors would be BR 45 O 60 30 74 4 1 1 2 2 3 3 12 1 2 2 23 3 2 2 2 5 i X 1 3 3

A person used force F shown in figure to move a load with constant velocity on a given surface Identify the correct surface profile 1 3 F A L L 2 4 L

18 A magnet is placed vertically on a paper Then the neutral point obtained on the paper is are 2 2 4 Zero 1 1 3 3

d 49 m Two bodies whose masses are in the ratio 2 1 are dropped simultaneously at two places A and B where the accelerations due to gravity are gA and go respectively If they reach the ground simultaneously the ratio of the heights from which they are dropped is a a gA SB b 2gA SB c gA 2GB d 8a gb

A stair case contains ten steps each 10 cm high and 20 cm wide The minimum horizontal velocity with which the ball has to be rolled off the upper most step so as to hit directly the edge of the lowest step is approximately 1 42ms 2 4 2ms 3 24ms 4 2 4ms 1

A belt is moving with constant speed u clockwise as shown in figure on two rotating fixed wheels The length of the belt between the wheels is 10 m as shown At time t 0 a small block starts moving from the upper right end of the belt with leftward speed v w r t ground u is friction coefficient between belt and block The moving part of the belt between the wheels is always horizontal Column I gives various values of u v u while column II gives the subsequent motion Column I FIXED 21 2 u 1 m s v 4 m s 0 2 u 5 m s v 2 m s 0 4 D u 2 m s v 1 m s 0 A u 1 m s v m s 0 1 P5 BOS P l 10 m P Q R S T FIXED Column II Block will fall off the left end of belt Block will fall off the right end of belt Slipping stops before block falls off the belt Block will fall off the belt at time t 1 1 sec Dl 111 6 11 663

Two bodies move in a straight line towards each other with initial velocities v and v and with constant accelerations a and a2 directed against their corresponding initial velocities The between them maximum initial separation for which they will meet during the motion is 1 2 4 1 4 v a 1 a2 V V 2 a a V1 V2 3 a1a2 max 2

21 A body is projected at t 0 with a velocity 10 ms at an angle of 60 with the horizontal The radius of curvature of its trajectory at t 1 s is R Neglecting air resistance and taking acceleration due to gravity g 10 ms 2 the value of R is a 10 3 m c 5 1 m JEE Main 2019 11 Jan Shift 1 b 2 8 m d 2 5 m

The equation of projectile is y 3x 2 horizontal range is 1 3 2g 3 g 2 3 2 4 2 3 g 1 3 g 2

Two trains moving at velocities u and u travel along the same line towards each other Drivers of both the trains when the trains are at a distance s apart simultaneously apply brakes producing retardations a and a2 respectively Prove that a collision can be avoided only if ua uza 2a a s

5 A stone dropped from a balloon at rest from a certain height passes through 81 m in the last before it strikes the ground Find the height of the balloon and the velocity of the stone when it hit the ground 5207 m 319 5 m s 5281 25 325 25

9 A particle starts from rest with acceleration 2 m s The acceleration of the particle decreases down to zero uniformly during time interval of 4 second The velocity of particle after 2 second is a 3 m s c zero b 4 m s d 8 m s 2

An object moving with a constant acceleration in a straight line travels from A to B At half time the posi where 3u v 3V u AP tion of the object is P Prove that BP u and v are the velocities at A and B respectively 9

2 Due to a strong 65 km h wind from the west a plane ends up traveling 330 km h S15W relative to the ground What is the velocity of the plane relative to the air Give speed and direction

36 A ship is moving towards N E with a velocity of 10 km hr and to a passenger on board the wind appears to blow from the north with a velocity of 10 2 km hr Actual velocity of the wind is 1 10 km hr towards N W 2 15 km hr towards S E 3 10 km hr towards S E 4 15 km hr towards N W

11 A particle moves along straight line for 10 second with uniform acceleration a 2 ms 2 Then for next 10 second moves with acceleration a 4 ms The total displacement of particle would be 1 400 m 3 550 m 2 500 m 4 650 m

22 A block of mass 1 kg is connected with a massless spring of force constant 100 N m At t 0 a constant force F 10 N is applied on the block The spring is in its natural length at t 0 ooooo a 4 cm s c 80 cm s t 0 V 0 m Find the speed of particle at x 6 cm from mean position F b 10 cm s d 50 cm

body us R Nx is directed towards the origin 4 Velocity is perpendicular tor and accelerat is directed away from the origin AIIMS 2016 A particle starts with angular accelerati 2 rad sec It moves 100 rad in a random inten of 5 sec Find out the time at which random inter starts 1 7 5 sec 3 5 sec eral 2 4 5 sec 4 6 sec NEFT LIG 2017 3 24 20 m 2 Three identi thread as sh moving in a outermost the three 1 3 5 2 3 4 3 7 4 3 N YN A pa

2 66 A stone dropped from a balloon at rest from a certain height passes through 81 m in the last before it strikes the ground Find the height of the balloon and the velocity of the stone when it hits the ground 5207 m 319 5 m s 5281 25 1 4 S

A particle passes a given point moving downwards with a velocity of 50 m s How long before this was it moving upwards at the same rate 1 12 s 3 10 2 s 2 18 2 s 4 15 4 s

from a very high tower Then the correct option is 10 m s A O B 10 m s 1 Distance between them is 20m at t 2s 2 Distance between them is 20 m at t 1s 3 Magnitude of relative velocity of A wrt B is 20 m s at t 2s 4 Magnitude of relative velocity of A wrt B is 10

21 For the small damping oscillator the mass of the block is 500 g and value of spring constant is k 50 N m and damping constant is 10 g s 1 The time period of oscillation is approx 1 2 S T 3 S 5 2 4 2 13 T S 155 S 2

A particle is moving Eastwards with a velocity of 5 m s In 10 S the velocity changes to 5 m s Northwards The average acceleration in this time is 1982 3M a zero 1 b m s towards North Eeast 2 31 31 m s towards North West c 2 d m s towards North

A person starts from his home on a straight road in his car at a speed of 50 m s for half an hour Then the fuel in his car finishes So he stops walks to a petrol pump some distance ahead on the same road He gets the fuel from the pump and gets back to his car in 20 min Then he again starts moving in initial direction of motion with same speed of 50m s What is the average velocity of the man in 1 hour after he started from his home 1 Zero 2 120 km hr

A particle is moving in xy plane in a circular path with centre at origin If at an instant the position of particle is given by 1 then velocity of particle is along 3 1 1 4 Either 1 or 2

Particle is projected upward It takes time to to reach projected vertically downward same point It takes time to reach released from reach the ground Then particle is to to with speed u from certain height the ground Another particle is same speed u From to reach the ground Third same point It takes time with

A car travels with a speed 12 m s while a scooter travels with a speed 36 km h Which of the two travels faster

A ship is moving due north across a river running towards west At the end of one hour it is found that the ship has made 8 3 km in a direction 30 west of north Find the speed of the ship 1 10 km hr 2 12 km hr 3 14 km hr 4 16 km hr

The velocity of a river current is u A man crosses the river with velocity v making an angle with the direc tion of the current If the width of the river is d find the time taken to cross the river and the displacement of the man in the direction of the current What would be the minimum time required for crossing the river In what time could he reach exactly the opposite point HS 05 d dcote I sin iranillos non dovr ons to d 1 1 214ucose 2uvcose

A car starts from rest and moves with constant acceleration The ratio of distance covered by the car in nth second to that covered in n second is 1 2n 1 2n 2 2 n 2n 1 3 2n 1 n 4 1 n

A car start moving with an acceleration 5 m s for 10 s then it decelerates with 2 m s Find the total distanc travelled by the car till it stops A 500 m B 625 m C 1125 m D 875 m

4 The graph given alongside shows the positions of a body at different times Calculate the speed of the body as it moves from i A to B ii B to C and iii C to D 5 What can you say about the motion of a body if a its displacement time graph is a straight line b its velocity time graph is a straight line 6 A body with an initial velocity x moves with a uniform acceleration y Plot its velocity time Th Gall Cl graph h for a moving Distance cm 76 7 6 5 2 T 0 2 3 B C 4 567 Time s

7 A particle thrown vertically up reaches at half of the maximum height in 2 1 second The speec of projection of the particle is g 10 m s 2 10 2 m s 4 40 m s 1 10 m s 3 30 2 m s

Locus of the path of a projectile in a vertical plane is given by y ax bx where a and b are constants and the horizontal and the vertical distances from the point of projection are x and y respectively Find the maximum height attained and the angle of projection a with the horizontal tan la 4b

50 The angles which the vector A 3i 6j 2k make with the coordinate axes are 2 12 1 a cos b cos 3 c cos in tit 7 14 13 1 COS 7 6 1 COS and cos 7 5 7 and cos 14 COS and cos 7 7 d None of the above 13 77371 3 91 3

3 A uniform rope of mass m and length is placed on a smooth table such that one fourth of its length hangs down The rope begins to slide down The speed of the chain when it completely slips of the table is 3gl V 8 3 15gline 2 1 neew 2 15gl 1600 16 slugele gl 4 9er C

Figure shows two blocks connected by a light string placed on the two inclined parts of a triangular wedge The coefficients of static and kinetic friction are 0 28 and 0 25 respectively at each of the surfaces a Find the minimum and maximum values of m for which the system remains at rest b Find the acceleration of either block if m is given the minimum value calculated in the first part and is gently pushed up the inclined for a short while g 10 m s Singl my 45 m 2kg 45 10

65 Water drops are falling at a regular interval of time from a certain height H above the ground At the instant the fourth drop is released the first one just reaches the ground The height of the third drop from the ground is 1 3 H 4 8H 9 2 4 H 9 3H 4

Two particles P and Q are launched simultaneously as shown in figure Find the minimum distance between particles in meters 10X X 2X2X15 A puolus 90m r 12m min 10ms P 45 10 2 10 2X 70ms H 70 x 70 x 1 45 2 X 2 X 10 35 2

34 A rod placed against a smooth wall on a smooth floor is sliding d velocities of points A and B then VB 1 B VA VB X y X A y 2 V V x y 3 VA Y V B X 4 V VB

A ball is dropped from a height of 5 m onto a sandy floor and penetrates the sand up to 10 cm before coming to rest If the retardation of the ball in sand m sec is 70n Assuming it to be uniform Find n

3 Two balls are projected from the same point in directions inclined at 60 and 30 to the horizontal If they attain the same height then the ratio of the velocity of projection is 1 1 1 2 1 3 3 1 2

A car moving with a speed of 25m s takes aU turn in 5 second without changing its speed The aver age acceleration during these 5 sec is

A body starts from rest with uniform acceleration of 10 m s for 10 second then it decelerates by 5 m s and comes to rest The distance covered by the body is 1 1000 m 3 2000 m 2 1500 m 4 2500 m

26 Positions of two vehicles A and B with reference to origin O and their velocities are as shown A they will collide C their relative speed is V 201 m s 100m 0 3 0 100 3m m s O 20 B 3jm s B distance of closest approach is 100 m 20 D their relative speed is m s

m me ble 19 ot the as an en 19 Ans 4 18 A boy runs on a horizontal road with a speed of 4m s while it is raining He sees that the rain is making an angle with the vertical while running from west to east However when he runs from east to west the angle is a The rain is pouring down at an angle 45 with the vertical and at a speed of 8 m tan 0 tan a s as shown in the figure The ratio Vernical ve 345 West A 12 B 8 C 1 62 D 1 6 2 is East 17

28 A ball is thrown at an angle 0 up to the top of a cliff of height L from a point at a distance L from the base as shown in figure Assuming that one of the following quantities is the initial speed required to make the ball hit right at the edge of the cliff which one is it A C gl 2 tan 0 1 gl cose 2 tan 0 1 B D cos 02 tan 0 1 gl tan 0 2 tan 0 1

A steamer is moving towards east with a velocity u A second steamer with a velocity 2u is moving at an angle north of east The second steamer is directed towards north east with respect to the first one Show that 0 1 sin 3 4 2

A steel ring of radius 10 cm and cross section area 1 cm is fitted to a wooden disc of radius 10 5 cm If Young s modulus of steel is 2 10 1 Nm 2 then the force with which the steel ring is expanded is in N 1 104 3 106 2 105 4 107

A lift starts moving upwards from ground with a con stant acceleration a cms 2 After ts a piece of stone is dropped from it Show that the stone touches the t a ground after a a g s g