Kinematics Questions and Answers

A thief is running away on a straight roa d on a bike moving with a speed of 20 ms 1 a police car initially at the rest st art chasing the thief with an acceleratio n of 2ms 2 The initial distance betwee n the thief and police to catch the thief

O A train moves from rest with acceleration a and in time t covers a distance x It then decelerates to rest at constant retardation for distance y in time t Then A X B C x y y a B B t a t D X Bt y at

The 2 kg ball is thrown at the suspended 20 kg block with a velocity of 4 m s If the coefficient of restitution between the ball and block is e 0 75 and the tune the collision lasts is 0 05 sec determine The maximum distance h the block will rise h The average normal force between the block and the ball during the collision F N

The velocity of a particle is v ati bt j where t is the time in second Match the columns for t 1 second Column I A Acceleration of particle is B Tangential acceleration is C Radial acceleration is D Radius of curvature of path is Column II 3 2 p less than a 6 3 q less than ab b r less than a b 2 2 s greater than 2h

A body of mass 3 kg acted upon by a constant force 1 is displaced by S metre given by relation S where t is in second Power of the force is 1 constant 2 linearly increases with time 3 Increases with time as 1 2 Im

Ek Columbian weed peddler ka circus tha kanpur mai waha uske pas ek bandar tha jo A cart se uchal ker B cart pe jatta aur fir B cart se uchal ker A cart per jatta last mai uski velocity btao Dono Cart rest pe hai pata hai tum bologe kuch to diya nahi to ye lo mass of bandar 4 Kg Mass of carts 20 Kg both same velocity of bandar wrt cart 6m s

A uniform rectangular metal plate ABCD is supported by two hinges P and P so that it remains in equilibrium in vertical plane with line AB vertical as shown in the figure The reaction forces R and R exerted by hinges on the metal plate is best depicted by D D R R P P B A P B 2 B P R D C R P B C

10 Two projectiles are thrown with different velocities and at different angles to cover the same maximum height Show that the sum of the times taken by each to reach the highest point is 3 equal to the total time taken by either of the projectiles

7 A balloon is ascending at the rate of 10 ms at a height of 40 above the ground when a food packet is dropped from the balloon After how much time and with what velocity does it reach the ground Take g 10 ms 8 A ball is thrown upward with an initial velocity of 100

A car travels a distance s km on a straight road in two hours and then returns to the starting point in the next three hours Its average speed in four hours in km h 1 3 5 5 2 4 2 5s 12 4 Zero

Cycling in Different Directions A boy is cycling at 20 km hr in a direction making an angle 30 north of east Find the velocity of a second boy cycling towards north so that to him first boy appears to be moving towards east

A Ball Clearing a Wall A ball is thrown from the ground to clear a wall 3 m high at a distance of 6 m and falls 18 m away from the wall Find the angle of projection of the ball

Hailstones Rebounding off From a Windscreen Ajungle safari Jeep has its front windscreen tiltable When hailstones fall vertically at speed 5 3 m s after bounding from the windscreen it is observed from jeep that hailstones rebound vertically If the windscreen is tilted at angle 60 with vertical find speed of jeep Consider elastic collision

From a 200 m high tower one ball is thrown upwards with speed of 10 ms and another is thrown vertically downwards at the same speeds simultaneously The time difference of their reaching the ground will be nearest to a 12 s b 6 s c 2 s d 1 s

28 The speed at the maximum height of a projectile is half of its initial speed of projection u The horizontal range of the projectile is 3 u 2g 4 2 Ja 3 u g 24 4 a 2

9 A body is projected from the top of a tower with a horizontal velocity 10 m s Taking g 10 m s2 how far away from the top of tower will it be after 2 seconds A 10 2 m C 30 2 m B 20 2 m D 40 2 m

SolveLancer Test A metal sphere of radius r falls vertically from a very large height Friction of air which depends directly on the speed of sphere acts on it due to which it attains a constant velocity It strikes the ground and bounces off e 0 5 What s the acceleration of sphere just after hitting the ground SolveLancer Test a 2g 4 b 1 5g c gl d 0 5g

Velocity time graph of two objects moving in same direction is given in the figure below Ratio of acceleration of object 2 to that of object 1 is Velocity 2 37 37 1 2 16 9 Time

4 Two buildings PT height 20m and SQ height 30m are at a distance I apart from each other A mass M is thrown horizontally from tower PT towards the other tower with a velocity of 10m s At the same time another mass 2M is thrown with the same initial velocity of 10m s from the tower SQ with mass 2M making an angle of 60 with the horizontal towards tower PT If the two bodies strike mid air and get attached to each other then the position where they hit the ground is A 11 57m and 5 77m B 11 03m and 6 30

Rain is falling with speed of 4 m s in the direction making an angle of 30 with vertical towards north What should be magnitude and direction of velocity c cyclist to hold his umbrella exactly vertical so that ra does not wet him 2 m s towards south 2 m s towards north 4 m s towards east

1 A particle of mass m and charge q has been projected from the ground as shown below V E A uniform electric field A The path of the motion is parabolic D The path of the motion of the particle is straight line

Estimate the probable number of persons in the income group 20 to 25 2 The distance covered by an athlete for the 50 meter race is given in the following table Time Sec 0 1 3 5 6 0 2 5 15 5 Distance meters Determine the speed of the athlete at t 3 sec 2 8 5 24 5 36 5 50

A box is kept on a rough horizontal surface and is at rest A horizontal force just strong enough to move the box is applied so that block starts moving This force is maintaine seconds and is then removed The total distance moved by the box is meter Then find the value of 8 Take 44 0 2 14 0 15 g 10m s S

12 In the arrangement shown P is movable pulley and is fixed pulley Block 1 is constrained to move freely P is in a vertical guide and block 2 can also move vertically When 0 60 if velocity of block 2 is v then velocity of block 1 will be 1 3 2V 3 2 0 P V 0 H P 2 2 V 2 4 3 V 2 2 V 3

Two uniform solid cylinders A and B each of mass 1 kg are connected by a light spring of force constant 200 N m at their axles and are placed on a fixed wedge as shown in the figure The coefficient of friction between the wedge and the cylinders is 0 2 Find the angle made by the line AB with the horizontal in equilibrium A 60 30

with minimum surface areas Example 34 4 Find the path on which a particle in the absence of friction will slide from one point to another in the shortest time under the action of gravity V T U 2004 PAT A TD 0445

A stone is dropped from a captive balloon at an elevation of 304 8m Three second later another stone is thrown vertically upward from the ground with a velocity of 75 6m s If g 9 81m s when and where the stones pass each other

A material point moving along a straight line enters an 87 5 m segmen with speed 5 0 m s and leaves with speed 10 m s The particle crosse the segment with unidirectional acceleration that never exceeds 1 m s Find range of average acceleration of the point on this segment

3 Two forces 3 N and 2 N are at an angle such that the resultant is R The first force is now increased to 6 N and the resultant become 2R The value of is HP PMT 2000 a 30 c 90 b 60 Lidy 120 10

A body is moving with velocity 30 m s towards east After 10 seconds its velocity becomes 40 m s towards north The average acceleration of the body is CBSE PMT Pre 2011 a 5 m s b lm s c 7 m s d 7 m s

A particle is thrown from top of a tower of height 50 m with velocity 30 m s at an angle of 30 with horizontal above the horizontal what is the time of flight of particle in seconds

Question 24 A person in a car moving with constant velocity of 15m s in positive x direction throws a ball such that the velocity of ball with respect to himself is parallel to y z plane At that time the car is 90m away from the origin The ball hits the target kept along y axis at 120 m from the origin If the car reaches the origin at the same time when ball hits the target then for the given condition here XY plane is horizontal 8 10m s car 90m Target 120m

A body starts from rest with uniform acceleration If its velocity after n seconds is v then its displacement in the last two seconds is A B D 2v n 1 n Your Answer v n 1 n v n 1 n 2v n 1 n

A ball is projected with velocity 202 m s at an angle of 45 with horizontal as shown in figure The ball collide 1 1 the wall thecoefficient of restitution between the ball and wall A is and with the wall B is distance of point 4 2 where ball collide with the ground from the projection point is e 1 2 e 1 4 U 20 2 m s 45 5m 10 m B

Rosemary attends Life Sciences Secondary School It took Rosemary 3 minutes to walk from school to the Q train The Q train is 150 meters west of her school On average how many meters did Rosemary walk for each minute Show your work Include UNITS and DIRECTION in your answer I Can you tell from the previous question whether Rosemary walked straight there or whether she took a detour Can you tell whether she speeds up or slows down Or is there additional information you would need Explain Use your answer to the previous question to explain why the quantity you calculated is called average velocity

A hollow vertical cylinder of radius R and height h has a smooth internal surface A small particle is placed in contact with the inner side of the upper rim at a point P It is given a horizontal speed vo tangential to the rim It leaves the lower rim at point Q vertically below P The number of revolutions made by the particle will be A B h 2 TR VO 2gh

5 Figure 28 E11 shows two adiabatic vessels each containing a mass m of water at different temperatures The ends of a metal rod of length L area of cross section A and thermal conductivity K are inserted in the water as shown in the figure Find the time taken for the difference between the temperatures in the vessels to become half of the original value The specific heat capacity of water is s Neglect the heat capacity of the rod and the container and any loss of heat to the atmosphere Figure 28 E11

The acceleration of a particle starting its motion from rest is function of velocity as per the equation a 2 3v where v is the velocity The velocity of the particle after a very long time will be

Q14 A train is travelling with a speed of 15m s and a man is walking inside the train at 1m s in the direction of train Find the velocity of man w r t to an observer on ground a 15 m s b 16 m s c 14 m s d 1 m s

7 A particle starts moving from origin in xy plane such that its instantaneous velocity in m s is v 5y i 2t where y and t are the instantaneous y co ordinate in m and time in sec respectively Find the locus of the particle 1 y5 x 3 y3 x2 2 y x5 4 y x

A lift of mass 500 kg is connected with a wire of breaking stress 108 N m TL If the lift moves up with an acceleration of 5 2 m s then calculate the minimum radius of wire so it does not break Take g 9 8 m s

12 An airplane is traveling directly east at a speed of 600 miles per hour There is a crosswind traveling 30 west of north N 30 W at a speed of 50 miles per hour a 5 points What are the velocity vectors of the plane and the wind in component form plane after influence from the wind

A plank having mass of 7 9 kg is resting on a smooth horizontal surface and it supports a block of mass 2 kg as shown in figure There is no friction present anywhere The value of the spring constant for the spring shown in the figure is 1000 N m If a bullet of mass 100 grams moving with a velocity of 400 m s hits the plank and gets embedded into it then find the maximum elongation of spring during the motion after the collision

dv Vo upwards erage velocity of on and highest 3cos 0 in 0 velocity glect air plane 4 tan 8 A ball is projected from the ground at angle 60 from the ground if ball just clears a wall 5 m from point of projection and falls on the ground 15 m away from it on other side then height of the wall is nearly equal to 1 5 8 m 2 6 5 m 3 7 9 m 4 98

agle 60 m from 15 m ewall the value of a is 1 0 28 2 0 38 3 0 48 4 0 58 A ball is projected at angle 0 45 from horizontal with speed u If after time t value of vertical component of velocity becomes equal to the value of horizontal component of velocity then 1 t sin 0 cos 0 g 2 t sine cose 3 t cose sine 4 t cose sine 9 5u 3g 18 If vector B is added to A the If B is subtracted from 41 71 then magnitude 1 4 1 2 3 2 3 8 2 4 2 0 16 The sum of two vector has magnitude 5 unit smaller vector then 1 13 unit 2 12 unit 3 10 unit 4 2 unit If a hody

darkened Zero Marks 0 If none of the bubbles is darkened Negative Marks 1 In all other cases Portion AB of the wedge as shown in figure is rough and BC is smooth A solid cylinder rolls without slipping from A to B The ratio of translational kinetic energy to rotational kinetic energy when the cylinder reaches point C is A 3 4 B AB BC B 5 75 C All India Open Test Nurture Course JEE Main 29122019 D 818 SPACE

3 1 3sin 0 4 1 3sin 0 An aeroplane is flying with constant velocity releases food packets from it then Neglect air resistance 1 It will always be vertically below the aeroplane 2 It will always be vertically below the aeroplane only if plane is flying horizontally 3 It will always be vertically below the aeroplane if it is flying at angle 60 to the horizontal 4 It will left behind the aeroplane gradually 5 A projectile is fired at some angle 0 with speed v 9 is nea 1 5 2 3 Tw bu op ba O

21 A projectile is thrown up with initial speed u making angle with the horizontal 0 45 Time just after which it will be moving perpendicular to its initial direction of motion is 2 3 4 60 1 3 4 u g sin e usine g u g cose ucose g 1 tan 2tar 2 tan tan 3 tano 1 tano t 2 1 4 26 To a station an angle 30 speed v m s of rain w r t 1 v m s 4 3 v 3 27 Two pa

1 Bx at a 2 ax B t 3 xt a 4 at B x 47 A ball is dropped from an elevator moving upward with acceleration a by a boy standing in it The acceleration of ball with respect to Take upward direction positive 1 Boy is g 2 Boy is g a 3 Ground is g 4 Both 2 3 48 A ball is thrown upward with speed 10 m s from the top of the tower reaches the ground with a speed 20 m s The height of the tower is Take g 10 m s

A body travelling along a straight line traversed one third of the total distance with a velocity 4 m s The remaining part of the distance was covered with a velocity 2 m s for half the time and with velocity 6 m s for the other half of time The mean velocity averaged over the whole motion is 1 5 m s 3 4 5 m s 2 4 m s 4 3 5 m s