Kinematics Questions and Answers

3 A person driving a car with a speed 72 km h suddenly sees a boy crossing the road If the dista by car before the person applies brakes is 5 m the reaction time of the person is 1 0 5 s 2 0 10 s 3 10 s 4 0 25 s RELATIVE VELOCITY

4 A particle starts with angular acceleration 2 rad sec It moves 100 rad in a random interval of 5 sec Find out the time at which random interval starts A 7 5 sec C 5 sec B 4 5 sec D 6 sec

A particle is moving in 3 dimensions Its position vector is given by T 61 3 4t 3 2t t k Find acceleration of particle at t 3s Also find tangential and normal acceleration at the same tim

4 10 Hz Preeti reached the metor station and found that the escalator was not working She walked up the stationary escalator in time t One other days if she remains stationary on the moving escalator then the escalator takes her up in time to The time taken by her to walk up on the moving escalator will be W t t t t 2 1 1 12 1 t t t t 3 t t 4

5 ALLEN Let r t 3ti 4t and F2 t 4t i 3tj 25 represent the positions of particles 1 and 2 respectively as functions of time t f t and F2 t are in metre and t is in second The relative speed of the two particles at the instant t 1 s will be 1 1 m s 3 5 2 m s 2 3 2 m s 4 7 2 m s 11 F t 3ti 41 1 2 are t 1 1 m s 3 5 2 m s feeff t 4 3 8 1 1 27 2 3 2 m s 4 7 2 m s

4 40 m s North A man is running up hill with a velocity 24 21 31 m s w r t ground He feels that the rain drops are falling vertically downwards with velocity 4 m s If he runs down hill with same speed find Vm velocity of rain with respect to man 1 2 2 m s 3 2 5 m s 2 2 3 m s 4 2 10 m s 4 40 m s 3 ft 3917 youfen fact 21 31 m s fa t een af 4 m s geh facft eft a grm 1 2 2 m s 3 2 5 m s af r av 2 2 3 m s 4 2 10 m s

3 W 4 W Three blocks with masses m 2m and 3m are 34 connected by strings as shown in the figure After an upward force F is applied on block m the masses move upward at constant speed v What is the net force on the block of mass 2m g is the acceleration due to gravity 1 zero 3 3 mg m 2 m 3 m 2 2 mg 4 6 mg 3 W1 4 W g dia sala feargun siten ari g fan s seu 41 m 2m 3mm in all a f m fa funt Ther 1 3 3 mg F m 2 m 3m g 2 2 mg 4 6 mg V

A speeder in an automobile passes a stationary policeman who is hiding behind a bill board with a motorcycle After a 2 0 sec delay reaction time the policeman accelerates to his maximum speed of 150 km hr in 12 sec and catches the speeder 1 5 km beyond the billboard Find the speed of speeder in km hr

26 3 5 2 m s 4 7 2 m s A particle moves along x axis such that its 26 position at time t is x 3r t m Total path length covered in first 4 sec is 1 16 m 2 24 m 3 12 m 4 None of above 3 5 2 m s 4 7 2 m s 3 faf x 31 t m 1 4 ferit 1 16 m 3 12 m 2 24 m 4 3

A block of mass 12 2 kg is sliding at an initial velocity of 4 90 m s in the positive x direction The surface has a coefficient of kinetic friction of 0 213 Indicate the direction with the signs of your answers a What is the force of kinetic friction in N acting on the block N b What is the block s acceleration in m s2 m s2 c How far will it slide in m before coming to rest

9 A boy sitting on the topmost berth in the 29 compartment of a train which is just going to stop on a railway station drops an apple aiming at the open hand of his brother sitting vertically below his hands at a distance of about 2 meter The apple will fall 1 Precisely on the hand of his brother 2 Slightly away from the hand of his brother in the direction of motion of the train a zat 3 Slightly away from the hand of his brother in the direction opposite to the direction of motion of the train 4 None of these 2 mar at from 1 2 f 3T 3 fe 4

22 ALLEN A particle is projected horizontally with a speed 22 20 m s from some height at t 0 At what of time will its velocity make 60 angle with the initial velocity 1 1 sec 3 1 5 sec 2 2 sec 4 2 5 sec 20 m s fa fen FIRMI fa fa 1 1 sec 3 1 5 sec 2 2 sec 4 2 5 sec 60 1 fener

Example 3 A kangaroo jump vertically What must be the initial velocity of the kangaroo Given a 9 8 m s s 2 5 m 0 y s u 2as 0 u 2 9 8 2 5 Negative sign is used as the acceleration is in the direc tion opposite to that of velocity 0 u 49 u 49

4 3 directed towards the origin 4 directed away from the origin A particle travels 10 m in first 5 second 10m in 14 next 3 second Assuming constant acceleration what is the distance travelled by particle in next 2 second 1 8 3 m 3 10 3 m 2 9 3 m 4 None of these 3 gefur af sine refera 4 10 FIT 8 1 8 3 m 3 10 3 m Prefera tag 10 este pret afta 2 9 3 m 4 None of these

4 18 In which of the following velocity time graph 18 magnitude of displacement is maximum 1 M N M N 2 2 af 2

Q 1 O A person who aims to reach the exact opposite point on the bank of a stream swims at a speed of 0 5 m s at an angle of 120 following the direction of the water flow What is the speed of water in the stream O 1 m s 0 25 m s 1 0 5 m s 00 09

A block of mass m is attached with a massless spring of force constant k The block is placed over a rough inclined surface for which the coefficient of friction is u 3 4 The minimum value of M required to move the block up the plane is Neglect mass of string and pulley and friction in pulley C 2 m 3 A m 5 B m 4 5 3 D m m 37 ooooooo M

W 135 J Ans The work done is 135 J Q 51 While decreasing linearly from 5 N to 3 force displaces an object from 3 m to Calculate the work done by this f during this displacement Solution For a variable force work done is giver

Q 6 O Two trains are each 50 m long moving parallel towards each other at speeds 10 m s and 15 m s respectively After what time will they pass each other O 2 5 sec 3 4 sec 2 sec 1 6 sec 00 03

Car A and car B are 20 km apart on opposite ends of a highway Car A started from rest then uniformly accelerated for 5 minutes where it reached a velocity of 30km hour where it maintained the said velocity for the remaining time of travel Car B started from rest and maintained a constant acceleration of 0 1 m s for its entire travel time When the ti cars meet How much distance is traveled by each car

Q 8 O A 150 meter long train is moving towards north with a velocity of 10m s A parrot is flying in the south direction parallel to train at 5m s The time taken by the parrot in crossing the train is O O 12s 8s 1 15s 00 02

The displacement of a particle moving in 15 a straight line is described by the relation S 6 12t 2t Here s is in metre and t is in second The distance covered by particle in first 5 second is 1 20 m 3 24 m 2 32 m 4 26 m 1 20 m 3 24 m 6 12t fatura 21 i fam es t 2 32 m 4 26 m

Q 5 O O A boat crosses a river with a velocity of 8 km h If the resulting velocity of boat is 10 km h then the velocity of river water is O 6 km h 8 km h 10 km h 1 4 km h 00 02 O

5 If the relation between distance x and time t is given as t ax Bx a and being appropriate constants then the retardation of the particle is v is the velocity of the particle 1 2av 3 2 Bv3 2 2B v 4 28

If the force acting on a body is inversely proportional its speed the kinetic energy of the body is A constant B directly proportional to time C inversely proportional to time D directly proportional to square of time

Q 10 A train of length 200 m travelling at 30 ms overtakes another train of length 300 m travelling at 20 ms The time taken by the first train to pass the second train is O O O O 30 sec 50 sec 10 sec 1 40 sec 00 00

A particle of mass 2 kg moves along x axis and if position coordinate varies wi th it find a Intial position b v t and init ial velocity C a t D Time at which it c hanges it s direction F Time interval du ring which particle accelerates and reg arts

The initial speed of a bullet fired from a rifle is 630 m s The rifle is fired at the centre of a target 700 m away at the same level as the target How far above the centre of target the rifle must be aimed in order to hit the target 2014 1 6 1 m 3 9 8 m 2 1 0 m 4 4 2 m

person moving with 8 moksle due East and Raindrops are falling with 2 vertical against his metion Find the angle at which he must 37 from vertical en up his umbrella to prevent the rain over him angle from vertical

14 A uniform cylinder of mass M and radius R is to be pulled over a step of height a a R by applying a force F at its centre O perpendicular to the plane through the axes of the cylinder on the edge of the step see figure The minimum value of F required is F 1 Mg 1 M 3 Mg TT FRY R a R R a 2 Mg 1 a a R

Choose the correct answer 1 If a 3i 4k and 6 6i 5j 2k then laxbl is 2 1 17 3 32 A particle experiences a force F kr f is the unit vector along position vector The dimensional formula of K is 1 MLT 3 M L T 2 27 4 37 2 ML T 2 4 ML T 3 Velocity time graph of a particle in straight line motion is in shape of a semicircle of radius R as shown in figure Average acceleration of particle from t 0 to t Ris V m s R t sec 4 5 1 Omanda 3 R m s A particle starts from origin at t 0 and moves in the x y plane with a constant acceleration a in the y direction The equation of motion is y kx Velocity component of particle along x direction is 1 Zero a 2k 2 1 m s 4 2R m s 3 3k Two projectiles A and B are projected with same speed at angles 15 and 75 respectively to the horizontal on ground Which of the following is correct 1 HA HB 2 HA HB 3 TA TB 4 Both 2 and 3 4

m s 1 0 3 R m s2 2 1 m s 4 2R m s A particle starts from origin at t 0 and moves in the x y plane with a constant acceleration a in the y direction The equation of motion is y kx Velocity component of particle along x direction is 1 Zero a 2 2k a WIN

3 t 6s and t 16s 4 A stone is thrown vertically upward from a bridge with an initial velocity of 4 9m s It strikes the water after 2s What is the height of the bridge from the water level g 9 8m s 1 19 6m 3 29 4m 2 9 8m 4 None of these

6 A particle is moving in a straight line such that its velocity varies as v voet where a and t are constant Find the average velocity during the time interval in which the velocity Vo 2 decrease from vo to ns o log 2

2 2 2 12 A spinning solid spherical ball having angular velocity is projected on a horizontal rough 2r surface with velocity vo The velocity of centre of mass of the ball when slipping ceases will be F 1 V 2 3 4

33 The equation for a wave travelling in x direction on a stretched string is given by y 5 cm sin 2x cm x 100m s f Acceleration of a particle at x 8 cm and t 0 11 s will be 1 20 x cm s 3 5x cm s 2 10 cm s 4 Zero

A light inelastic thread passes over a small frictionless pulley Two blocks of masses m 1 kg and M 3 kg respectively are attached with the thread and heavy block rests on a surface A particle P of mass 1 kg moving upward with a velocity of 1 10 m s collides with the lighter block and sticks to it The speed of the bigger block just after the string is taut will be g to A B 10 ms D P M 1 2 5 m s 5 ms 4 m s s 1 2 ms 1 Correct Answer

5 The potential energy of a particle having mass 1 kg is given by U 4x 3y Joule where x and y are in metre If the particle was at rest at 16 6 at time t 0 then speed of the particle when it crosses x axis 1 10 m s 3 2 5 m s 2 5 m s 4 15 m s

A boat which is moving downstream passes a raft and moves 10 km ahead of raft in next one hour and then return upstream with same speed relative to river and meets the raft after the raft has moved 10 km If the same boat wishe to cross the river without any drift then the angle boat should row with stream velocity is tan 2 B KIN tan 1 2 C sin D 120

sin 0 cos 0 tan 0 m OA 40 90 4 0 m T 0 m BC 0 90 10 70 3 10 5 2 30 9 32 2 AB 90 Ot dec 10 6 3 17 OT INC 2 O decreasing 107051 2 1 2 2 1 7 3 1 0 8 tamo not defined m 0 3 0 9 2 0 5 CD 0 90 m M tan O O 2 O 3 O DE 90 0 71 0 11 1 OT INC 2 30 B Of der 2 osl 2 20 61 1 3 1 45 INC lo 3 2 D 0 E 0 In which part slope of graph is continuously increasing y 1 only in OA 2 only in AB 3 in BCD 3 60 90 89

C 8 km hr When a balloon is at a height of 80 m ascending with a velocity of 10 m s and acceleration 1 2 m s2 drops a packet Find the time taken by the packet to reach ground Take g 10 m s DIE 300

22 Car P is just behind car Q Both are 5 m long The Velocity of car P is 54 km h and that of Q is 36 km h Find the road distance travelled by Car P to cross Q A 15 m B 20 m D 35 m C 25 m

A parachutist drops freely from helicopter for 20 s before the parachute opens out Then he descends with retardation of 40 m s2 The height of the helicopter from the ground level is 2500 m When he drops out his velocity on reaching the ground will be 1 10 ms 1 2 10 10 ms 3 20 ms

A ball falls freely from rest and the total distance covered by it in the last second of its motion is equal to the distance covered by it in first five seconds of its motion The total time of the ball when it is in motion would be 1 16 5 s 3 15 s 2 17 s 4 13 s

From the top of a 11 m high tower a stone i s projected with speed 10 m s at an angle of 37 with the horizontal find T Time of flight note i already got the answer but have a do ubt while solving if i take g to be negative as the object is fallling down answer comes ou t to be 11 5s whereas if i take g as positive the answer comes out to be 1 how to know what to use as both the answers are differe

Three different objects of masses m1 m2 and m3 are allowed to fall from rest and from the same point O along three different frictionless paths The speeds of the three objects on reaching the ground will be in the ratio of 1 m m2 m3 2 m 2m2 3m3 3 1 1 1 4 1 m1 1 m2 1 m3

A steel wire can withstand a load up to 2940 N A load of 150 kg is suspended from a rigid support The maximum angle through which the wire can be displaced from the mean position so that the wire does not break when the load passes through the position of equilibrium is 2008 E 1 30 2 60 3 80 4 85

A particle of mass 2 kg moves on the x axis under the influence of force of attraction acting towards the origin given by F 7 If the X particle starts from rest at x 4 m the speed it will attain to reach the point x 2 m will be 1 1 m s 2 2 m s 3 m s 4 m s

7 A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northwards with same speed v The two particles coalesce on collision The new particle of mass 2m will move with velocity V 1 North East 2 V 3 North West V 2 V South West 4 North East

C A car starting from rest at constant acceleration covers a distance S in a time interval t It covers a distance of S in the next time interval t at the same acceleration Which of the following relations is true 2 A S 2S 2 C S 3S B S S 2 1 D S 4S 2