Kinematics Questions and Answers

HOTS Problem 1 Four persons K L M and N are initially at rest at the four corners of a square of side d Each person now moves with a uniform speed v in such a way that K always moves directly towards L L directly towards M M directly towards N and N directly towards K Show that the four persons meet at a time dlv Solution All the four persons will meet at the centre O of the square Each person covers a displacement 1 Problems on Higher Order d d 2 Component of velocity v towards O v cos 45 v 2 Required time S V t K N d 2 v 2 V 45 v cos 45 Fic

Two boats A and B having same speed in still water are moving in a river A moves normal to river current as observed from ground B moves normal to river current as observed from the river frame Then A For a ground observer B is moving faster than A B For a ground observer A and B are moving with same speed C For an observer in river frame B is moving faster than A D For an observer in river frame A and B are moving with same speed

A bullet is fired with a velocity of 500 m s in a direction 20 above the horizontal Given that its acceleration is a gj where g 9 8 m s and it is initially at 0 0 find its velocity v at any time t seconds

tan 13 6 is at a point P whose coordinates are Bird observes two points P and P 1 m 2 m 0 m and 1 m 1 m 4 m 0 it starts flying in a plane of three ant speed of 5 ms in a direction might line P P till it sees P and P late t tion is shown in Fig 4 95 The on perpendicular to line P P point Q in time after starting sees P and P as collinear m 4 m 7 B 9 4 95 26 6 e P 1 m 2 m 0 m 2 67 m 4 583 Time taken by bird to reach the point Q will be d 2 67 0 5346 s V 5 3 kmh finds that wind seems to blow from north On Problem 4 A person travelling eastward with a speed of doubling his speed the wind appears to flow from north east Find the magnitude of the actual velocity of the wind Solution The situation is shown in Fig 4 96 North West Wind 6 km h 3 km h 45 Fig 4 96 Let the wind velocity be v 90 8 North East Man East of wind makes an

A rigid rod of length is sliding At some instant position of the rod is as shown in the figure End A has constant velocity vo At t 0 y l y wall B 0 X A floor X Component of velocity of end B along the length of the rod as a function of time t is Graph of y as a function of time t is a parabola Velocity of end B as a function of time t is vo t y Graph of y as a function of time t is an ellipse

A boat is being steered across a river flowing at 4 m s The river has a width of 100 m In each of the cases shown in List I the velocity of boat in still water is 2 m s In List II we indicated the possible values of time taken to cross the river Match them 1 11 IV List l The boat is being steered to minimize the time taken to cross the river The boat is being steered to minimize the drift The boat is being steered at an angle of 30 to the river flow The boat is being steered at an angle of 120 to the river flow O LP 11 S III RIV Q OP RIIDR IV Q LUIRIRIV Q OP Q R IV Q P Q R S T U List I 50 sec 58 sec 100 sec 120 sec 20 sec 40 sec

A particle starts moving at t 0 in x y plane such that its coordinates in m relate with time in sec as x 2t and y 5 sin 2t aximum speed of the particle is O 12 m s 29 m s 2 26 m s

go for NEET 46 A block slides down an inclined plane of inclination O with constant velocity It is then projected up the inclined plane with an initial speed u How far up the incline will it move before coming to rest 1 s 4g sino 3 2 u gaine

WEET NURTURE PHASE I TO III INTERNAL TEST 05 02 09 2020 The pendulum hanging from the ceiling of a railway carriage makes an angle 30 with the vertical when it is accelerating The acceleration of the carriage is 1 SI L O

A light string going over a clamped pulley m supports a block of mass M as shown in t The force on the pulley by the clamp is gi 1 2 Mg 2 2 mg 3 g M m m 4 g M m M m M

SN 5 3 N 4 5 3 N SN mass is hanging on a spring balance which is ot in a lift at rest shows some reading If the lift ends with increasing speed at constant rate e spring balance will show in its reading Increased Decreased No change Change will depend upon velocity body of mass 2 kg is hung on a Spring balance

1 BALL BOUNCE A pingpong ball dropped from a height of 10 feet Each time it hits the ground it bounces to 80 of its previous height ft 8 0 ounce S TI IL number 4 096 ft 4 096 ft a Find the total distance traveled by the pingpong ball E

An aeroplane flies round a square field PQRS of each side 1000 km Its speed along PQ is 400 km h along QR 500 km h along RS 600 km h and along SP 700 km h The average speed of the aeroplane over the entire trip A 550 km h C 527 km h B 600 km h D 500 km h

The friction of the air causes a vertical retardation equal to 10 of the acceleration due to gravity Take acceleration 10m s The maximum height and time to reach the maximum height will be decreased by

along a straight line is as shown in the figure At what time the particle acquires its initial velocity a m s 10 1 12 s 2 5 s 4 3 8 s t s 4 16 s

A particle is projected from a tower of height H with a speed of 50 m s at an angle of 37 with the horizontal Then select the CORRECT alternative s take point of projection as origin 0 0 3 Equation of trajectory of particle is y x x 320 25 Particle moves perpendicular to initial direction at 3 sec O Minimum speed of particle in subsequent motion is zero Maximum height attained by the particle from the point of projection is 45 m

A boy rides a bicycle back and forth along the ground and the horizontal position of the bicycle is given below Position no 30 30 BO Time seconds a Find the displacement and the distance covered by the bicycle between 0 second and 30 seconds Ans 90km 90km b Calculate the displacement and distance travelled by bicycle between 0 second and 40 seconds Ans 30km 150km c Calculate the displacement and distance travelled by bicycle between 30 seconds and 50 seconds Ans 30km 90km d What is the total displacement and distance travelled by bicycle Ans 60km 180km

22 Consider a gravity free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow 8 ft above the floor of the hall He pushes the pillow down so that it starts falling at a speed of 8 ft s The pillow makes a perfectly elastic collision with the floor rebounds and reaches the experimenter s head The time olanced i nt th

Two man a and b starts from a common point on a circular track of radius 5m in opposite direction with speed 1m s and 2m s respectively If they move for a very long time At how distinct point will they meet

Example 6 3 Pulleys shown in the system Fig 6 244 are massless and frictionless Threads are inextensible The mass of blocks A B and C are m 2 kg m 4 kg and m3 2 75 kg respectively Calculate the acceleration of each block 06 Fig 6 244

A car moving with an initial velocity of 5 mph accelerates at the rate of a t 2 4t mph per second for 8 seconds a How fast is the car going when the 8 seconds are up b How far did the car travel during those 8 seconds

A bead of mass m is located on a parabolic wire with its axis vertical and vertex directed toward downward as in figure and whose equation is x ay If the coefficient of friction is the highest distance above the x axis at which the particle will be in equilibrium is a Find the value of n 4

Velocity v time t graph of a particle moving along a straight lin is shown in the figure The average velocity of the particle from t to t 4 sis v m s 4 0 4 2 20 m s 10 m s O 5 m s Zero 4 t s

A ball is thrown vertically upward from the roof of a tall building with an upward speed of 15 m s Find the ball s velocity when it is 5 m above the building O 10 m s O 11 2 m s O 7 m s O there is no answer O 8 m s

The 18 Two balls are dropped from the same at two different places A and B where the and SB acceleration due to gravities are ga body at B takes t seconds less to reach the ground and strikes the ground with a velocity greater than at A by v m s Then the value of v t is 1 3 1 SASB 1 SASB 2 2 SASB 4 SASB

Q 29 A force of 21 73 Newton is applied to a body of 5 kg mass for 10 seconds The initial velocity of body is 23 m sec Find the value of final momentum of body f 2 fj m 5kg 10 11 21 A 25 kg m sec B 60 kg m sec C 85 kg m sec D 65 kg m sec Q

In figure shown a boat can move with 10 m s in still water If it steers as shown then it will reach other shore To reach at point B it can B O move at the same angle without changing speed move with same speed with greater angle move with greater speed at same angle move with greater speed at greater angle 800m 10 37 8 m s

man walking downhill with velocity u finds that his umbrella gives him maximum protection from rain when he holds it such that the stick is perpendicular to the hill surface When the ma ns back and climbs the hill with velocity u he find that it is most appropriate to hold the umbrella stick vertical Find the speed of raindrops w r t ground The inclination of the hill is 0 30 52 m s 0 30

An elevator is moving upward with a constant speed of 10 m s A man standing in the elevator drops a coin from a height of 2 5 m from floor of elevator The coin reaches the floor of the elevator after a time sec t 2 What is the value of t

A thin rod of mass m and length is hinged to a ceiling and it is free to rotate in a vertical plane A particle of mass m moving with speed v strikes it as shown in the figure and gets stick with the rod 2 60 m The value of v for which rod becomes horizontal after collision is Im 168 9 gl The value of v for which rod becomes horizontal after collision is 53 3 ge Angular momentum of rod particle system will remain constant about hinge just before and after collision Angular momentum of rod particle system will remain same about centre of mass just before and after collision

In figure a hollow tube of mass M is free in horizontal direction The system is released from rest There is no friction present The tube and blocks are taken as system i Momentum of the system is conserved in x direction ii Speed of A w r t M speed of B w r t M iii Acceleration of centre of mass along X axis is constant iv Centre of mass has finite acceleration Evaluate the above statements and choose the correct option from the following m A M 723 B A Statements i ii are true and iii iv are false B Statements i ii are false and iii iv are true

A disc of radius 50 cm is rolling purely on a horizontal ground with velocity of ceutre of mass 10 mg 10 ms What is the instantaneous speed of point P as shown in diagram 10 ms O P A 10 ms B 10 2ms C 20 ms D 5 ms

bomb is projected vertically upward from ground At heighest point it explodes in two parts having mass ratio 1 2 Both the part lanc n ground at equal distance from point of projection at on interval of 4 sec If both parts land on ground at time t and t2 after explosion 1 1 nd 5

1 Two ships A and B are at rest on still water of a sea Ship B is at a position 80 km east and 150 km north of A Ship B starts moving with a velocity of 10 km hr towards west and at the same time ship A starts moving with velocity components 30 km hr and 50 km hr along east and north respectively After what time interval the distance between two ships will be the minimum

Least possible value of correction factor for i kinetic energy is zero ii kinetic energy is 1 momentum is zero iii iv momentum is 1 sd The correct statements are a i and iii b c ii and iii i and iv ii and iv

A man walking downhill with velocity u finds that his umbrella gives him maximum protection from rain when he holds it such that the stick is perpendicular to the hill surface When the man turns back and climbs the hill with velocity u he find that it is most appropriate to hold the umbrella stick vertical Find the speed of raindrops w r t ground The inclination of the hill is 0 30 u 52 m s

A particle is projected from ground at an angle 9 At a certain instant the velocity vector of particle makes an angle a with horizontal g dv modulus of gsina dt Tangential acceleration has magnitude of g sin a Normal radial acceleration g cos a

Illustration 5 60 Two particles are located on a horizontal plane at a distance 60 m At t 0 both the particles are si multaneously projected at angle 45 with velocities 2 ms and 14 ms respectively Find 1 u 2 m s A 45 ik 60 m B42 14 m s 45 B Fig 5 122 a Minimum separation between them during motion b At what time is the separation between them minimum

A particle is thrown upward with speed 10 3 m s It strikes the inclined surface as shown in figure If collision is perfectly inelastic find maximum height of particle from ground g 10 m s 45 3m 10 3 m s

14 A ball is thrown from the top of a 10m high tower at an angle 600 from the vertical with a velocity 10m s Find the distance from the base of the tower to the point where it falls and the time taken to do so g 10m s 3

30 A coconut from nearby coconut tree suddenly fell down The type of motion executed by the coconut is neglecting air resistance Uniformly accelerated motion Non uniform motion Uniform motion None of these 31 The area under velocity time graph of the motion of coconut gives Initial velocity Final velocity Height of the coconut tree Acceleration due to gravity

Two particles X and Y of equal mass and with unequal positive charges are free to move and are initially far away from each other With Y at rest X begins to move towards it with initial velocity u After a long time finally A X will stop Y will move with velocity u B X and Y will both move with velocities u 2 each C X will stop Y will move with velocity u D both will move with velocities u 2

23 The tension in the string connected between blocks is F 10 N 2 kg 7777 Xx 80 N 3 ay 50 N 4 kg 77777 Smooth surface Aakash Educational Services Pvt Ltd Read Officer A 40 N 26 N F 20 N

32 When Raju was travelling with a velocity of 10 m s a cat came in front of his car Suddenly Raju applied the break of his car and car stopped with a retardation of 5 m s2 Find the stopping distance of the car O 5m O 10 m O 15 m 20 m

Read the following passage and the answer the following questions Raju was on a long trip He got trapped in a traffic jam During that time he was retrieving his Class 11 Physics memories Let us go along with his memories and try to find the answers of the following five questions 28 The motion of a car during a traffic jam is an example for Uniform motion Non uniform motion Uniformly accelerated motion 4 None of these 29 Raju suddenly thought of his friend Ramu who was a good athelete during school days Ramu completed a running race by running on a circular track by coming back to the starting point without reversing the direction in 68 s What was the displacement covered by Ramu in that race O Tr O 2 r O o

A A body is at rest at x 0 At t 0 it starts moving in the positive x direction with a constant acceleration At the same instant another body passes through x 0 moving in the positive x direction with a constant speed The position of the first body is given by x after time t and that of the second body x after the same time interval Which of the following graphs correctly describes x x as a function of time 1 3 12 x L X 2 4 X X 2 X1 X 2

2 A is a thin walled sphere at rest made up of glass The radius of the sphere is Im and it is filled with a transparent liquid of refractive index S is the luminous source moving directly towards a plane vertical mirror M A fish in the liquid is moving towards S The eye of the fish and S and collinear perpendicular to mirror M At the instant shown S is 3m away from the center of the sphere fish observes that image of S due to reflection is moving with speed of 13m s If speed of the fish relative to the sphere is 10m s and 1 5 then find the speed of the source at that instant The system is placed in air Fish THE NARA GR A GROUP

50 A dipole consists of two particles one with charge 1 C and mass 1kg and the other with charge 1 C and mass 2kg separated by a distance of 3m For small oscillations about its equilibrium position the angular frequency when placed in a uniform electric field of 20kV m is A 0 1 rad s C 10 rad s B 1 1 rad s D 2 5 rad s

A particle initially at rest is moving on a straight line If s v F P and t denote displacement velocity force power and time respectively then Column I Column II D A P constant B F constant 1 C Foc 3 P 3 S Q xt R cs

3 An object is thrown up in the air At time t measured in seconds the height of the object is h t 50t 16t2 measured in feet Find the velocity of the object at the following times t 1 and t 3 Interpret the sign of the velocity in each case