Kinematics Questions and Answers

1 Mg equilibrium against a smooth vertical wall and a rough horizontal surface If 0 be the angle of inclination of the rod with the horizontal then normal reaction of the wall on the ladder is 2 3 4 Mg 2 tane Mgcot 0 3 Mg 0 rough smooth

A particle starts from rest and moves along x axis The acceleration a varies with its displacement x as a 2 x m s Find magnitude of acceleration of particle when its displacement along positive x axis is maximum O 1 m s O 2 m s O 4 m s O 3 m s

A ship of mass 3 x 107 kg initially at rest is pulled by a force of 5 x 104 N through a distance of 3 m Assume that the resistance due to water is negligible the speed of the ship is A 1 5 ms B 60 ms C 0 1 ms 1 A force of 5N acts on a body of weight 9 8N What is the acceleration produced in D 5 ms

from a clif A ball is thrown horizontally such that it strikes the ground after 5s The line of sight makes an angle 37 with the horizontal The initial velocity of projection in ms is 1 50 100 2 T 3 100 F 4 100

Two particles A and B are at corners of the field A moves with velocity 3 m s at an angle of 60 to the line AB Find the angle in degree made by B with AB so that it catches A Assuming speed of B as 3 3 m s

An object is thrown vertically upward Which one of the following statements is false At the top of the trajectory the acceleration vector is zero When the object is moving downwards the velocity vector and the acceleration vector are in the same direction When the object is moving upwards the velocity vector and the acceleration vector are in opposite directions At the top of the trajectory the velocity vector is zero

1 7 pts A man runs at a constant speed of v 5 m s along a straight road A car that was initially at rest starts moving toward the runner at the moment when the distance between them is d 200 m as shown in the figure As the car moves toward the runner it gradually increases its speed with a constant acceleration of magnitude 0 50 m s a Write the kinematic equations for position x and velocity v 1 for the runner b Write the kinematic equations for position x and velocity v r for the car c From the moment it starts moving how much time does it take for the car to reach the runner d What distance will the car have traveled when it reaches the runner e What is the speed of the car when it reaches the runner

A police van moving on a highway with a speed of 30 km h and a thief s car speeding 2 away in same direction with speed is 192 km h Thief in the car fires bullet on police van If muzzle speed of bullet is 150 m s then the speed with which bullet hits the w r t police van is NCERT Pg 58 2 130 m s 1 145 m s 3 115 m s 4 105 m s The acceleration of a body starting from rest

3 4 5R A particle of mass m is projected from orly speed u at an angle 8 with positive x axis Posit y axis is in vertical upward direction Find angular momentum of particle at any time tab O before the particle strikes the ground again 1 m ucose gtk 2 m ucose gt k

Two athletes A and b participated in a race along a circular path with constant speed o f 11 m s and 13 m s respectively B reache s the finish line in 2 seconds earlier than a what is the radius of the circular path

A bomb of mass 3 0 kg explodes in air into two pieces of masses 2 0 kg and 1 0 kg The smaller mass goes at a speed of 80 m s The total energy imparted to the two fragments is 1 1 07 kJ 3 2 4 kJ 2 2 14 kJ 4 4 8 kJ

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency The amplitude of oscillation is gradually increased The coin will leave contact with the platform for the first time A At the highest position of the platform B At the mean position of the platform C For an amplitude of g m

How h 1 2gtxt when the projectile is at same height at di fferent time intervals t o t t ttz 2 h gt t igtitz tmax B u Copex ti T titt 2usine g Rahul Work New Section T t t V total displacemt total time u 0 t t t t ZV copo

A body of constant mass m 1 kg moves under variable force F as shown If at t 0 S 0 and velocity of the body is 20 m s and the force is always along direction of velocity then choose the incorrect options boboig 16JP110144 S 10 N F N mont bos doome is savo grigned anopisyd ballug ai gante en to 2m S m 6m A velocity of the particle will increase upto S 2m and then decrease B the final velocity at S 6 m is 10 m s mas C the final velocity at S 6 m is 4 5 m s the acceleration is constant up to S 2m and then it is negative DRZW option Kaise hoga Ye Do o

Continuing with the situation if the force F 80 N is directed vertically as shown the acceleration of the 1 kg block will be T A 2 m s2 towards right C 6 m s towards left 10 kg C 0 6 Smooth Rods are light 15 kg light rods xxx mmmmmmmmrus B 2 m s towards left D 16 5 m s towards right F 80 N

Figure shows the graph of x coordinate of a particle moving along x axis as a function of time Average velocity during t 0 to 6 s and instantaneous velocity at t 3 s respectively will be m 20 10 X 0 1 2 3 4 5 6 1 10 m s 0 t s 2 60 m s 0

9 The sum of magnitudes of two forces acting at a point is 16 N Their resultant is 8 3 N and is at 90 with the force of smaller magnitude Calculate the magnitude of the smaller force in Newton

other part will move with speed 1 20 m s 2 10 13 m s 3 50 m s 4 30 m s A ball of mass m approaches a wall of mass 22 M m with speed 4 m s along the normal to the wall The speed of wall is 1 m s towards the ball The speed of the ball after an elastic collision with the wall is 1 5 m s away from the wall 2 9 m s away from the wall 3 3 m s away from the wall 4 6 m s away from the wall 1 20 m s 3 50 m s 34 2 1 5 2 9 3 3 4 6 2 10 13 m s 4 30 m s Mar ai a a dar ga

For a gas sample with No number of molecules function N V is given by N V 3 V for dN dV V 0 V V and N V 0 for V Vo Where dN is number of molecules in speed range V to V dV The rms speed of the molecules is A B Vo Correct Answer Your Answer Vo DU

45 180 On an open ground a motorist follows a track that turn to his left by an angle of 72 after every 1000 m Starting from a given turn the displacement of motorist at forth turn is 1500 m 1000 m 1732 m 4000 m

A uniform rod of length and mass m is free to rotate in a vertical plane about a wedge A The roc initially in horizontal position is released The initia torque acting on the rod with respect to wedge is l 3l 44 A

A ball thrown upward from the top of tower with speed v reaches the ground t1 second If this ball is thrown downw ard from the top of the same tower with speed v it reache s the ground in t2 second In what time the ball shall reac h the ground if it is allowed to fall freely under gravity fro m the top of the tower A t t 2 B t t 2 C t t D t t

A man can swim with a velocity v relative to water He has to cross a river of width d flowing with a velocity u u v The distance through which he is carried downstream by the river is x Which of the following statements are correct du A If he crosses the river in minimum time x V du B x cannot be less than V T C For x to be minimum he has to swim in a direction making an angle of 2 the direction of the flow of water T D x will be maximum if he swims in a direction making an angle of 2 sin u with with the

A stone is thrown vertically upwards with a velocity of 19 6 m s After 2 second another stone is thrown upwards with a velocity of 9 8 m s When and where will these stones collide take g 9 8 m s

1 2 1 15 16 3 1 m s 3 m s H 4 5 in metres 6 2 7 Above diagram represents a multiflash photograph of an object P moving along a horizontal surface The successive positions as indicated in the diagram are separated by equal time intervals of 1 second The first flash occurred just as the object started to move and the last just as it came to rest The average speed of the object during the motion is 8 16 15 4 0 9 m s 9 m s 10 X2 1202 619 2

34 The horizontal range and the maximum height of a projectile are equal The angle of projection of the projectiles is 4 c 0 tan 2 a 0 tan by0 tan 4 d 0 45 AIPMT Pre 12

a 45 km h A table clock has its minute hand 5 0 cm long The average velocity of c 3 14 x 104 cm s hand between 6 00 am to 6 30 pm is ns 1 a 1 1 x 104 cm s b 2 2 x 10 4 cm s 1 tip of the minute d 3 3 x 104 cm s takes to prom

9 The initial velocity of a particle is u at t 0 and the acceleration a is given by af 2 Which of the following relations is valid 1 v u at 2 2 v u 3 at 2 2 3 v u at 5 45 2 4 v 1 5 2 11

An astronomer observes galaxy A moving away with B 0 55 and galaxy B moving away in exactly the opposite direction with B 0 65 What is the value of for the relative speed of galaxy A with respect to galaxy B Give answer to three significant figures

x axis between reflecting walls at x 0 and x a Between these two limits it moves freely at constant velocity v If the walls are perfectly reflecting then its displacement time graph is A B C D displacement displacement displacement Hisplacement 0 0 a v 2a v 3a v time a v 2a v 3a v time time

Block A B C connected with light string with larger block M as shown in figure Pullies are light and frictionless There is no friction anywhere Which is the correct FB D of larger block of mass M A C T T2 T T N Mg T AN T De Mg T1 B T2 T2 N Mg D None of these T1 m B in bas M Smooth surface

The velocity field in a two dimensional unsteady flow is given by v x y t 2xy 3xyj m s The magnitude of acceleration of fluid particle located at x 1 m y 1 m at the time t 1 s in m s is

A body moving with uniform retardation covers 1 5 km before its speed reduced to half of its initial value It comes to rest in another 11 m 11 7 m 11 2 m 1 km 11 5m 2 km A particle starts with an initial velocity 3 m s along the positive X axis and it accelerates uniformly at the rate of 0 60 m s The distance moved by it in first three seconds is 3 km 1 1 12 km 3 1 A car moving with a velocity of 80 km hr is slowed down to 44 km hr in 15 s The retardation is 4 0 67 m s 1 m s 1 25 m s 1 5 m s reach a velocity of 9 m s of 0 60 m s How much is the time taken by it to positive x axis and it accelerates uniformly at the rate A particle starts with an initial velocity 3 m s along the 2 A car moving at 72 km hr is stopped by applying breaks with a distance of 50 m The retardation experienced by car is 5 4 m s 2 m s 3 m s O 1 m s

9 A projectile is thrown with a velocity of 20 m s at an angle of 600 with the horizontal After how much time the velocity vector will make an angle of 450 with the horizontal in upward direction is take g 10m s A 3 sec B 1 3 sec C 3 1 sec D None of these

angle Two stones A and B are thrown simultaneously from a point on horizontal ground The stone A is thrown vertically up with velocity u and the stone B is thrown with speed up at 37 with horizontal After 0 9 S stones are moving perpendicular to each other Then A u 9 ms B u 9 ms C ug 15 ms D ug 9 ms

The velocities of A and B are marked in the figure 2 183 The velocity of block C is assume that the pulleys are ideal and string inextensible A 5 m s B 2 m s C 3 m s D 4 m s 1 m s AO m s B

1 A projectile is fired with a speed u at an angle 0 above the horizontal field The coefficient of restitution between the projectile and field is e Find the position from the starting point when the projectile will land at its second collision 1 2 3 e u sin 20 8 1 e u sin 20 8 1 e u sin cose 8 1 e u sin 20

n this question the y component of vel ocity of rain is in downwards direction o in answer the y component will be wi n negative sign one of these 10 A man starts running along a straight road with uniform velocity observes that the rain is falling vertically downward If he doubles his speed he finds that the rain is coming at an angle to the vertical The velocity of rain with respect to the ground is

0 4 2t a b 4 What is the average velocity of a projectile between the instants it crosses half the maximum height if it is projected with a speed u at an angle 0 with the horizontal 1 u sin 0 2 u cos 0 3 u tan0 4 H

268 A projectile is thrown with a speed u at an angle 0 to the horizontal The radius of curvature of its trajectory when the velocity vector of the projectile makes an angle a with the horizontal is TAMANNA CHAUDHARY 4

The velocity vector of a particle moving in xy plane is given by v ti xj If initially the particle wa at origin then the equation of trajectory of th projectile is 1 2x 9y 0 3 2x 9y 0 2 9x 2y 0 4 9x 2y 0

Consider an apple of mass m and that falls off a tree A common model for its speed v t after t seconds that takes air resistance into account is mg v t m 1 el c m C Here g is the acceleration due to gravity and c is some positive constant a Calculate lim v t Your answer may involve the constants c g and m 1 00 b For fixed t calculate lim v t Your answer may involve the constants c g and t m 400

k Solvelancer Test Which is the correct statement for the following structures Solvelancer Test CH T CH CH CH CHO I H C CH CHO Butanal 2 Methyl butanal a i and ii chain isomers b i and iii chain isomers c ii and iii position isomers d All are position isomers a b C d ii CH C CH CH 2 Butanone SolveLancer Test Which of the statement is correct for the given s t sraph 1 From 0 to t velocity is in negative direction II From 0 to t velocity is in negative direction III acceleration is negative throughout the motion 0 IV direction of velocity remains constantlSolvel ancer Testl t

D A car going at 22 metres per second passes a motorcycle at rest As it passes the motorcycle starts up accelerating at 3 2 metres per second squared If the motorcycle can keep up that acceleration how long will it take for it to catch the car a 12 s c 20 s b 14 s d 18 s

Two billiard balls of same size and mass are in contact on a table A third billiard ball of same size a mass strikes them symmetrically and come to rest after impact Coefficient of restitution betweent balls is 1 2 mc 2 3 3 4

19 1 25 m 2 45 m A stone is dropped from the top of a tower If it travels 34 3 m in the last second before it reaches the ground find the height of the tower g 9 8 m s 1 39 2 m 2 58 8 m 3 78 4 m 4 98 m ath second What is the fall of height in the next second

5 Blocks A and B are initially in equilibrium The springs and strings are ideal The accelerations of the blocks A and B just after the spring 2 is cut are respectively 1 g 0 al Answor 3 2 g g 2 Spring 1 2m B eeeeee Spring 2 Am 3 g g 4 0 g

28 particle moves along x axis in positive direction Its acceleration a given as a cx d where x denotes the x coordinate of particle c and d are positive constants For velocity position graph of particle to be of type as shown in figure the value of speed of particle at x 0 should be 1 4d C 2 C 3 2d C P 8d C

11 A stone weighing 3 kg falls from the top of a tower 100 m high and buries itself 2 m deep in the sand The time of penetration is 12 ant 2 0 9 sec 1 0 09 sec 3 2 1 sec The velocity of a body at any instant is 10 m s Aftor 5 acceleration is 4 none of these 4 1 3 sec

Example 2 A car is moving along a straight line OP It moves from 0 to P in 18 seconds and returns from P to Q in 6 seconds where OP 360 m and OQ 240 m What are the average velocity and average speed of the car in going a from O to P and b from O to P and back to Q EVA 6