Kinematics Questions and Answers

10 A drunkard is walking along a straight road He takes 5 steps forward and 3 steps backward followed by 5 steps forward and 3 steps backward and so on Each step is 1 m long and takes 1 second There is a pit on the road 11 m away from the starting point The drunkard will fall into the pit after 1 21 s 3 31 S 2 29 s 4 44

option marks In the diagram a plank of mass M is placed on a horizontal frictionless surface Two blocks of masses 4M and M are placed on the plank For both blocks the coefficients of static friction with the plank equal 0 16 and the coefficients of kinetic friction equal 0 10 The blocks are connected by a light string through a light pulley which is acted upon by an unknown horizontal force F The acceleration of the plank is 2 m s 4M The acceleration of block of mass M is 8 m s The acceleration of block of mass 4M is 2 m s The force F 1 8 Mg The friction force acting between the plank and the block of mass M is 0 1 Mg M F

For each question Full Marks 3 I ONLY the correct answer is chosen Zero Marks 0 In all other cases child in a boat needs to cross the river The speed of the current in the river is k 3 times greater than the speed of the boat in still water If a child crosses the river in such a way as to minimize the lateral displacement t estimet 3 2 sec to cross Find the minimum time in sec required to cross the river I Backspace

A ball is projected from ground with speed v1 in vertically upward direction It moves to a maximum height and returns back to it s initial point with speed v2 t1 and t2 are time taken by the ball for upward and downward journey respectively A resistive force of constant magnitude directed opposite to instantaneous velocity of ball acts on the ball during it s flight Choose the CORRECT option s A t1 t2 B t1 t2 C v1v2 t1t2

se with or without selection of any correct option s will result in 2 marks A fixed re coilless cannon fires a shell with a speed at the same instant a man falls from rest from point O The shell hits a point on the wall Initially shell is aimed towards a point P as shown in figure Mark the correct option s 0 The falling man sees the shell move along straight line directed along initial velocity Time taken by shell to reach the wall is b Vo cos 00 0 Sh

A bus moves from stop A to the next stop B Its acceleration varies as a a x where a and are positive constants and x is the distance from the stop A The distance between A and B and the maximum speed of the bus are a 24 and B 88 b and u c and B 2a B d 2 and R V2 2 B ariable Acceleration a da fvdv of adr a x vdv a px xn Bn dx 2021 7 29 09 3 B V2 dx v dv a z di X1 V1

Graph shown represents motion of a particle moving along positive x axis Find the average speed in m s of the particle during the time interval in which it move from x 0 to x 20m 1 3 A 4 B 2 1 10 20

time graph of a particle for the interval of t 0 to t 4s is given Which of the following option s is are CORRECT s m 0 1 2 B 3 4 A Particle reverses the direction of it s motion at t 2s Maximum distance of the particle during the motion from it s initial

4 56 CALC An object of mass m is at rest in equilibrium at the origin At t 0 a new force F 1 is applied that has components F 1 k k y F 1 k3t where k k and k are constants Calculate the position 7 7 and veloc ity 1 vectors as functions of time

A boat is traveling due east at 12 m s A flag on the boat flaps at 53 N of W Another flag on the shore flaps due nort Speed of wind with respect to ground is 16 m s Speed of wind with respect to ground is 20 m s Speed of wind with respect to boat is 20 m s Speed of wind with respect to boat is 16 m s 4

of 80km s Net force exerted on the rocket just about to tak 1 16 000 N 2 1 60 000 N 3 1 80 000 N A man slides down on a telegraphic pole with an acceleration equal to one fourth of acceleration due to gravity The frictional force between man and pole is equal to in terms of man s weight W 4 1 40 000 N 1 W 4 00 2 3W 4 3 W 2 4 W omall boat of mass 140kn which is at rest throws a 5kg stone in the after

A particle is thrown vertically upward with a speed of 20 ms 1 When it returns to point of projecti a its average speed is 5 ms b its average velocity is zero c its average acceleration is 10 ms d None of these

A bullet moving with a speed of 72m s enters a thick fixed wooden block and comes to rest after penetrating through a distance of 9 cm If the wooden block were 8 cm thick find the speed in m s with which the bullet would come out of the block Assuming constant retardation of bullet in wood A 12 2 m s B 24 2 m s C 24 m s D 8 3 m s

21 A ball is projected on a level ground such that its range is 20 m An observer moving parallel to the plane of projection observes range of 10 m relative to himself The ball has an initial velocity of 10 2 m s There are two values of velocity of observer for which it possible Find sum of velocities if they have same starting point

To f 11 A 10 kg collar P slides with negligible friction on the fixed vertical shaft When the collar is released from rest at the bottom position shown it moves up the shaft under the action of the constant force F 200N applied to the cable The position of the small pulley at B is fixed Find the spring constant k in k N m which the spring must have if its maximum compression is to be limited to 0 4 m 12m k 0 4m 5m P B

SolveLancer Test A particle of mass 2 kg which is initially at rest starts moving on a horizontal smooth surface with an acceleration which is a function of time and is given by a kt4 Find work done by the applied force in the first 1 second SolveLancer Test k a J 25 b J 25 k3 c J 25 k4 d J 25

A collar of negligible size slides over the surface of horizontal circular rod for which coefficient of friction is 0 3 The collar is projected with a speed of 4 m s and the radius of the ring is 10 cm The distance moved by the collar before coming to rest is g 9 8 m s 1 0 6 m 2 0 3 m 3 1 m 4 2 m

Particle A is moving with a constant velocity of V 50 ms in positive x direction It crossed the origin at time t 10 s Another particle B started at 1 0 from the origin and moved with a uniform acceleration of ag 2 msin positive x direction a For how long was A ahead of B during the subsequent journey b Draw the position x time 1 graph for the two particles and mark the interval for which A was ahead of B

A lift starts from rest at t 0 and moves upwards with constant acceleration of 5 m s At t 2 s a bolt from the ceiling of lift detaches and falls freely If height of lift is 7 5 m then the bolt hits the floor of lift at t n s Find the value of n g 10 m s Buses ply from city A to city B at regular interval of 15 minutes Every bus from A to B moves with constant

A body is just being revolved in a vertical circle of radius R with a uniform speed The string breaks when the body is at the highest point The horizontal distance covered by the body after the string breaks is A 2R B R C R 2 D 4R

There are two cars on a straight road marked as x axis Car A is travelling at a constant speed of V 9 m s Let the position of the Car A at time 1 0 be the origin Another car B is L 40 m ahead of car A at 1 0 and starts moving at a constant acceleration of a 1 m s at 1 0 Consider the length of the two cars to be negligible and treat them as point objects AV 9 m s Ba 1m s X x 0 K L 40 m a Plot the position time x 1 graph for the two cars on the same graph The two graphs intersect at two points Draw conclusion from this b Determine the maximum lead that car A can have

Example An insect of mass m crawls on earth s surface with velocity v at angle north of east The latitude of place where insect is situated is If to be angular velocity of earth s spinning motion and R be radius of earth Calculate centrifugal and coriolis force on the insect Velocity of insect w r t earth

A massless and inextensible string connects two masses m and 4m and the system rests on a smooth horizontal floor An impulse J is imparted to B as shown in figure The tension in the string in the subsequent motion is A Om 1

moving along x axis from origin with initial velocity of 3 m s The acceleration ac the particle varies with position x as a Kx2 where K is a constant At x 3 m the tangent to the graph makes an angle of 60 with x axis Then a x 3 m v represents velocity of particle a position x a m s 0 1 v 3 2 m s 2 V v 9 3 m s 160 3 a 3 m s x m

A ball is thrown up in the sky at what position will the instantaneous speed be minimum O O O Initial position Final position Halfway through the whole trajectory After covering one fourth of the whole traiector

Which of the following can be used to describe how fast an object is moving along with the directi of motion at a given instant of time O Instantaneous velocity O Instantaneous speed O Average velocity Average speed

A block A and wedge B connected through a string as shown The wedge B is moving away from the wall with acceleration 2 m s2 horizontally and acceleration of block A is vertical upwards Then B

A bullet is fired on to a wall with a velocity of 50 cm s If the bullet at the depth of 1 cm inside the wall Find the retardation produced by the wall a 12 5 ms b 12 5 ms d 32 5 ms c 20 5 ms

1 A train engineer drives a train 235 km north along a straight track Then he drives the train back south 126 km Finally he drives north again 45 0 km to his final destination What is the engineer s total displacement

Example A person is standing at the edge of a disc of radius R The disc is rotating about its axis with OR relative 2 uniform angular velocity w The person throws a stone in radially outward direction with speed for the disc Calculate acceleration of stone as seen by the person soon after throwing neglect gravity

2 Q 41 A point moves in a straight line so that its displacement x at time t is given by x t 1 Its acceleration is 2 a b 1 x d 1 x L 2 a 1 x c 1 x The displacement x of a particle varies with time

36 A ball is thrown vertically upward with a speed v from a height h metre above the ground The time taken for the ball to hit ground is 2hg 2 tr V b 2 2hg v2 1 fet 9 V3 a 9 c 1 2hg d 1 1 2h 2 v 9 2 v ition of a particle along X axis at time t is 2hgo

A thin ring of mass m and radius r rolls without slipping across the floor with a speed v with respect to ground Which of the following would be the best estimate of the ring s total kinetic energy as it rolls across the floor as seen from a frame moving in opposite direction with the same speed v with respect to ground A mv B 2 mv mv D None of these

22 Marks 9 A de shunt Motor running light takes current of 4A and run at speed 660 r p m the Ra is 0 3 ohm and that the Rsh is 270 ohm 50 h p 37 3 kw 460 v Determine whine the motor running at full load 1 The current in put 2 The speed determine the armature current at which efficiency is maximum

25 A ball of mass m is released from A inside a smooth wedge of mass m as shown in the figu mu m v cos45 u B 2gR of the wedge when the ball reaches point B 1 2 Lmv 2 mu mgh A 31 12 gR C 5gR 2 3 1 2 D 3 gR 36 A B 45 smooth

A particle is moving on a circular path of radius 6 m Its linear speed is v 2t here t is time in secor v is in m s Calculate its centripetal acceleration at t 3 s Two particles move in concentric circles of radii r and r2 centre Find the ratio of their angular velocities such that they maintain a straight line throu 1 order to have same cent

A ball is dropped from height h on an inclined plane of an gle of inclination alpha Find where it should strike on the s econd time on the plane The coefficient of restitution is e

A particle covers a distance unidirectionally with uniform acceleration If its average velocity is Uav what could be range of modulus of its instantaneous velocity at the midpoint of the path

A projectile is thrown from O on an inclined plane as shown in figure 4 It hits the plane perpendicularly 10 7m s B 30 1 2 3 4 figure 4 If projectile is thrown at time t 0 then time when projectile will be at a maximum distance from O is 1s 2 s 3 s 4 s g 10m s AnouOK

A gun has muzzle speed 150 m s Find two angles of elevation that can be used to hit a target 780 m away Enter your answers as a comma separated list Round your answers to one decimal place Use g 9 8 m s 9 9 8 1 4 x

A particle of mass m is connected to two springs of unstretched length 7 and spring constant k as shown in figure Calculate acceleration of particle if it is slightly displaced along X direction

A magnet falling vertically under gravity passes through a metal ring on its way Which of the following true about the acceleration a of the magnet where g denotes the acceleration due to gravity A a g everywhere B a g before crossing the ring and a g after crossing the ring C a g before crossing the ring and a g after crossing the ring D a g everywhere

Example A small asteroid is approaching a massive star with a speed v from very large distance at an impact parameter b as shown in figure If the mass of the star is M and its radius is R then what is the minimum value of b such that the asteroid will miss the star

28 A thin cylindrical rod of uniform mass density rests against a smooth wall as shown in figure Find the coefficien of friction between ground and rod if the minimum angle that the rod can make with the horizontal is 0 1 3 Lcos 0 sin 0 2 2h L cos 0 sin 0 Lcose sine 2h cos Asin A 0 2 4 Lcos 0 sin0 2h Lcos 0 sine Lcos0 sin 0 2h Lcos 0 sine

A man can swim in still water at a speed of 3 km h He wants to cross a river that flows at 2 km h and reach the point directly opposite to his starting point a In which direction should he try to swim that is find the angle his body makes with the river flow b How much time will he take to cross the river if the river is 500 m wide

A body of mass m rests on a horizontal plane with the friction coefficient At the moment t 0 a horizontal force is applied to it which varies with time F kt where k is a constant vector Find the distance traversed by the body during first seconds after the force action began

A tank with uniform cross sectional area A is filled with a liquid of density p upto a height h What is the potential erergy stored in the system where g denotes the acceleration due to gravity A Agph B Agph C Agph D Agph

In a car race on straight road car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B Both the cars start from rest and travel with constant acceleration a and a2 respectively Then v is equal to

12 The position time graph of a uniform motion in one dimension of a body cannot have negative slope Reason In one dimensional motion the position does not reverse so it cannot have a negative slope O a O b c O d

X c x 0 v 0 a d x 0 v 0 a 0 53 In one dimensional motion instantaneous speedv NCERT satisfies 0 v vo a The displacement in time T must always take non negative values The displacement x in time T satisfies Vo 1 x vol c The acceleration is always a non negative number d The motion has no turning points Exempla ont of a particle is given by 60 1 in second Th