Kinematics Questions and Answers

A B and C are three rafts floating in a river such that they always form an equilateral triangle A swimmer whose swimming speed is constant swims from A to B then from B to C and finally from C to A along straight lines Time taken by the swimmer is maximum in swimming From A to B From B to C From C to A 03 B River flow It is same in all the parts

Figure shows velocity time graph v m s 10 0 10 2 Average velocity for entire journey is 2 5 m s Average acceleration from t 1 to t 4 is 5 m s Average speed for 1st 4 sec is zero 6 Acceleration at t 3 ser is 5 m s t s

A block of mass 5kg released from rest on the top of the smooth inclined plane which is fixed to table as shown in figure It then slides on a rough horizontal surface of 0 2 for 1m It then leaves the top of the table which is 20 0 m high How far from the base of the table does the block lands 1m 5kg fixed 45 H 0 20m 1m 0 2 X

Find the incorrect option for given v t graph 20 A 10 B 10 D 20 30 40 E G 50 60 70 F 1 In AB DE and GH velocity and acceleration have same direction 2 Total distance in ABCDEFG is 600 m 3 acceleration in BC and EF is zero changing its

A car is moving with speed 72 km h on a straight road Suddenly brakes are applied due to which car retards at the rate of 10 m s distance travelled by car before coming to rest is 20 m 200 m O 260 m 190 m

Example 18 An object accelerates uniformly from initial velocity u to final velocity v It travels distance s in time t Then check the dimensional consistency of the following equations Which of them are correct physically U V 3 s ut at 2s

Two fixed frictionless inclined plane making an angle 30 and 60 with the vertical are shown in the figure Two block A and B are placed on the two planes What is the relative vertical acceleration of A with respect to B

Before jumping from the bridge Martin throws his water bottle to a friend standing on the bank of the lake The bridge is 7 0 m high The friend is standing on the bank 15 0 m from the base of the bridge with their hand 1 0 m above the ground What speed must Martin throw the bottle horizontally for it to reach his friend s hand 71 LJ

The parallax of a far off planet as measured from the two diametric extremes on the equator of the earth is 2 0 minute If the radius of the earth is 6400 km find the distance of the planet from the earth Angle of parallax 2 minute

A car is moving with 54 km h speed at t 0 Its break produces the retardation of 2 5 m s If he applies break at t 0 and produces constant retardation till car stops then the displacement travelled by car in X 10 sec is X Fill

A particle P performs circular motion such that its position vector F makes an angle 0 with x axis according to following equation e F 6t 8 rad Att 0 particle is at point A Particle changes its direction of motion only once O Particle does not change it s direction of motion Angular acceleration of particle is constant

A circus joker throws vertically three balls one after another with an interval of 0 5 s After 0 5 s of throwing the third ball he catches the first ball When he catches the first ball then A the height of second ball is 2 5 m B the velocity of second ball is 2 5 ms in upward direction C the height of third ball is 2 5 m D the velocity of third ball is 2 5 ms in downward direction

25 N force is applied to the block as shown in figure Choose the correct option s if initial velocity of block is zero Normal contact force is 20N Friction force is 5N Friction force is 10N Block is in equilibrium 37 2kg 25N s 0 5 0 4

Ball A is projected from tower of height 30 m and B is projected horizontally at 6 m s A and B collide in air If separation between the towers is d 10x What is the value of x 30 m s 30ml 53 6 m s 60m

INTRODUCTORY EXERCISE 7 2 1 A particle is projected from ground with velocity 40 2 m s at 45 Find a velocity and b displacement of the particle after 2 s g 10 m s 2 Under what conditions the formulae of range time of flight and maximum height can be applied directly in case of a projectile motion 3 What is the average velocity of a particle projected from the ground with speed u at an angle a with the horizontal over a time interval from beginning till it strikes the ground again 4 What is the change in velocity in the above question 5 A particle is projected from ground with initial velocity u 20 2 m s at 0 45 Find a R H and T b velocity of particle after 1 s c velocity of particle at the time of collision with the ground x axis 6 A particle is projected from ground at angle 45 with initial velocity 20 2 m s Find a change in velocity b magnitude of average velocity in a time interval from t 0 tot 3 s Fig 7 14 7 The coach throws a baseball to a player with an initial speed of 20 m s at an angle of 45 with the horizontal At the moment the ball is thrown the player is 50 m from the coach At what speed and in what direction must the player run to catch the ball at the same height at which it was released g 10 m s 8 A ball is thrown horizontally from a point 100 m above the ground with a speed of 20 m s Find a the time it takes to reach the ground b the horizontal distance it travels before reaching the ground c the velocity direction and magnitude with which it strikes the ground 9 A bullet fired at an angle of 30 with the horizontal hits the ground 3 0 km away By adjusting its angle of projection can one hope to hit a target 5 0 away Assume the muzzle speed to be fixed and neglect air resistance 10 A particle moves in the xy plane with constant acceleration a directed along the negative y axis The equation of path of the particle has the form y bx cx where b and c are positive constants Find the velocity of the particle at the origin of coordinates

In a cyclotron the potential difference of AC source connected across dees is 1000 V An a particle is accelerated in this cyclotron If it completes 200 revolutions then kinetic energy attained by a particle is O 0 2 MeV O 0 4 MeV O 0 8 MeV O 0 3 MeV

A stone is thrown with a horizontal velocity of 15 ms from the top of the tower If the stone hits the ground at a distance of 100 m from the foot of the tower calculate the height of the top

A projectile is projected with a speed an angle 30 with the vertical The speed of the projectile when its direction of motion makes an angle 30 with the horizontal is 1 10 m s 110 12 m s 2 20 m s 4 20 3 m s

A particle moves along a circle of radius R with speed varies as v aot where ao is a positive constant Then the angle between the velocity vector and the acceleration vector of the particle when it has covered one fourth of the circle is A tan 1 4 C tan B tan D tan 2

16 A particle is thrown with speed u at projection 0 with horizontal as shown in figure Choose the correct statement y O u A B C X D 1 Average velocity during O to D is ucose 2 Average velocity between A and C is ucose 3 Vertical components of velocities at A and C are a pair of negative vectors All of these

9 If a particle is moving along a straight line and its velocity varies with time as v 2t t v and t are in Sl units then choose the incorrect option 5 1 Average velocity from t 0 to t s is 2 5 m s 12 2 Acceleration is zero at t 1 s 3 Acceleration is 2 m s2 at t 0 m s 4 A Average speed from t 0 to t 2 sis 3

35 For a projectile projected from ground at an angle 0 with horizontal gT where T is time of flight 2R 3 R is horizontal range of projectile g is acceleration due to gravity The angle of projection 0 is 45 41 30 2 60 3 45 4 90

5 A particle is thrown vertically up such that distance travelled by it in 2nd second and 9th second is same Maximum height upto which the particle rises is g 10 m s 1 80 m 42 125 m 3 180 m

A car travels with speed 3 m s 1 for the first half distance of the journey and with speed 6 m s 1 for the remaining half What is the average speed of the entire journey NCERT Pg 42 1 6ms 1 3 9 m s 1 2 18 m s 1 1 1 m s 1

A stone is projected from a balloon which is ascending with a velocity 1 m s The velocity of the stone w r t balloon is 3 2 m s at an angle of 45 with the horizontal as well as with the vertical upward direction Find the magnitude of velocity of stone with respect to ground

22 1 12 second 2 8 second 3 15 second 4 10 second For the corresponding a t graph Draw the v t graph The particles starts from rest 1 2 3 2 K R 41 2 t t a 2 4 t Upuard represent positive and dou war

Two pulley one 600 mm diameter and other INVO 300 mm diameter are on parallel shaft 3000 mm apart and are connected by a open belt Find the length of the belt required and angle of contact between the belt and pulley

9 A lift is moving with velocity 10 m s upward with acceleration 5 m s2 upwards At the same instant of time a coin is dropped from 7 5 m above the floor of lift find distance travelled by the coin in ground frame before it strikes the floor A 5 m upward B 10 m downward C 10 m upward D 5 m downward

A block is released from rest on an fixed incline plane from a height 6m above the ground as shown in figure where coefficient of friction between block and incline plane is 0 5 Choose the correct option s for motion of block from shown position to the bottom of incline Change in potential energy is 300 J Work done by normal is 400 J Work done by friction is 200 J Final velocity of block when it just reaches to bottom of incline plane is 2 10 m s 6m 5kg fixed 37

An object is projected from point O with initial velocity U in vertical plane A mirror Mforms the image of object as shown Time after which relative velocity of object w r t velocity of image is least U M E 30 30 3g 2U 3g U

The maximum angle to the horizontal at which a stone can be thrown so that it always moves away fr the thrower will be atfavi v 37fdcbqTH fb u U U Uret th ch bd TIf Us g th a ER T A sin 1 C sin 2 3 1 B sin 1 D sin 1 2 2 3

8 A swimmer can swim in still water at a speed of 15 km h A river is flowing at 5 km h The swimmer starts from a point and swim 1 km upstream and then returns by swimming downstream back to original position During this the average speed of his her swimming is 1 20 3 km h 2 10 km h 40 3 km h 1 km 4 20 km h 11 15 4

3 A particle is thrown in air following trajectory y ax 3x where a and B are constant x and are horizontal line and vertical line respectively It s angle of projection maximum height 4x B 1 tan a Ans 2 Sol For Ymex X Ymay 20 Hmay dy dx 8 23 x 0 ax 2 tan a RED INS 8 3 tan 3 a 4 tan B B 4a an

A ring which is initially placed at the height h as measured from its center rolls down an inclined plane making an angle with the horizontal starting from rest The radius and mass of the ring are a and m find the angular velocity of the ring as it reaches the bottom of the inclination a b c d g V h r tan e g h r 2g h r g h r

Two particles A and B moving in X Y plane are at origin at t 0 sec The initial velocity vectors of A and B are A 81 m s and B 8j m s The acceleration of A and B are constant and are aA 21 m s and a B 2jm s Column I gives certain statements regarding particle A and B Column Il gives corresponding results

A particle is thrown horizontally with speed 10 m s along the rim of a smooth fixed cylinder of height 20m Taking g 10 m s2 the time taken by the particle to reach the bottom assuming it to be always in contact with the cylinder is in sec 10m s 20m

6 A particle moves along a straight line such that its displacement at any time t is given by S t 6t2 3t 4 metres The velocity when the acceleration is zero is Ra S t 612 3t 4 1 3 ms 1 2 12 ms 1 3 42 ms 1 4 9 ms 1

A uniform rope of mass 2 kg and length 4 m connecting two blocks is placed on frictionless horizontal ground The block of mass 3 kg is pulled by a 27 N force as shown in the figure What is tension in newtons at a point 1 away from the 1 kg block 50 3 kg 27 N

Question given below has answer in Numerical Value You need to enter the Numeric Value using your keypad For CORRECT Value there is NO NEGATIVE marking No marks will be deducted if you leave question unattempted 1 A particle moves along the positive branch of the curve y 4 2x where x x and y are 2 measured in metre and t in second At t 3s the velocity of the particle in m s is

Question given below has four answer options out of which ONE OR MORE is are correct For all CORRECT options selected you will be awarded 4 Marks ar each correct option selected provided NO INCORRECT option is selected For WRONG answer there is a NEGATIVE marking of 2 Marks No marks will be dec unattempted A stone is thrown from a point at a distance a from a wall of height b If it just clears the wall the maximum height reached by the stone if the angle of projection is a is A B C D a sec a 4 a seca b a tan a 4 atana b a tana 4 a bcota tan a

Negative Marks 1 In all other cases A swimmer crosses a river of width d flowing at velocity v While swimming he keeps himself always at an angle of 120 with the river flow and on reaching the other end he finds a drift of d 2 in the direction of flow of river The speed of the swimmer with respect to the still water is O 2 3 v 2 2 3 v O4 2 3 v O 2 3 v

Q On a two lane road car A is travelling with a speed of 36 km h Two cars B and C approach car A in opposite directions with a speed of 54 km h 1 each At a certain instant when the distance AB is equal to AC both being 1 km B decides to overtake A before C does What minimum acceleration of car B is required to avoid an accident NCERT 1 m s

Three particles A B and C situated at vertices of an equilateral triangle all moving with same constant speed such that A always move towards B B always towards C and C always towards A Initial seperation between each of the particle is a O is the centroid of the triangle Distance covered by particle A when it completes one revolution around O is Burm y Hhalg fayu yull a end up Rea laa Aud uld u SA Y r Ja f AB B a Car CA HAG D H GH GU HEY ARCH OR H Y SU AERI I T GR SIN DINK JO yg huh 0 h uka Ych adche of a A 2a 1 e 2 37 2a 2 3 u a u B C a 1 e 2a 3

A body travels the distance AB with speed 2 m s Thereafter it travels BC with speed 1 5 m s and the remaining CC 1 1 with 0 5 m s Calculate the averag speed for this journey assuming that t body takes some time in travellin distances BC a CC same 2x2x1 3 1 2 m s 2 1 33 m s 3 0 66 m s 2M 3 AH

29 A car P is moving with a uniform speed of 72 km h towards another car Q at rest on a straight level road At a particular instant when the distance between P Q is 525 m the car Q started accelerating at 2 m s towards P Find the distance travelled by Q when both the cars meet 525 1 300 m 2 20 2 225 m 525 3 100 m 4 30 m x t P 20m 5 23 12 XO 525m

Two cars A B start from rest from the same point in same direction with acceleration 8 m s2 4 m s respectively then acceleration of car B in frame of A Take direction of motion of car is positive In the previous question when distance between both cars becomes 200 m find distance travelled by the car A in ground frame

marks For a particle of mass 1 kg moving with a constant acceleration in any interval of time when initial and final velocities are u and v the average velocity is u v 1 2 the average velocity is u v 2 the average kinetic energy 2 U IS 1 u uv the average kinetic energy is

A bomber flying upward at an angle of 53 with the vertical releases a bomb at an altitude of 800 m The bomb strikes the ground 20 s after its release If g 10ms 2 the velocity at the time of release of the bomb in ms is 2 1 400 2 800 3 100 4 200

Supe A block rests on an inclined plane making an angle of 30 with the horizontal The coefficient of static friction between block and the plane is 0 8 If the frictional force on the block is 10 N then mass of block in kg Take g 10 m s 2 2 5 4 1 5 1 2 0 3 4 0

2 The position of a particle moving along x axis given by x 2t 3t 5 m The acceleration of particle at the instant its velocity becomes zero is 1 12 m s 2 12 m s 3 6 m s 4 Zero