Kinematics Questions and Answers

14 If a particle is moving on a straight line then its velocity time graph is sinusoidal as shown in the figure Velocity ms 1 T 2 Time s

A bead slides down a height on a rigid thin vertical rod in time T and same height on T a rigid helix in time T total distance covered by bead on rigid helix is I Find ratio T h 2 m 1 4m friction is absent everywhere Te

in a straight line under the retardation a which is given by a bv If the initial velocity is 2 m s the distance covered in time t 2 seconds is 1 blog 4 e 3 blog 1 4b 2 log 1 4b 1 4 log 4b 1

u a 25 kmh 24 mh in 18 A body starts from rest and moves with constant acceleration for t second It travels a distance x first half of time and x2 in next half of time then 9 x4 wors Ca x x c x 3x x2 KCET 2014 b x 2x x 4x on of a moving body is found from the Kerala CEE 201

3 a d c 4 a b d 17 Two bodies move in a straight line towards each other at initial velocities V and V and with constant acceleration a and a directed against the corresponding velocities at the initial instant The maximum initial separation max between the bodies for which they will meet during the motion is V V 2 a a 1 3 V V a a V V Jaaz 2 V V a a

slope of e area under acceleration time graph 20 A stone falls freely under gravity It covers distances h h and h3 in the first 5 s the next 5 s and the next 5 s respectively 43 x y 2 2 5

Fortnightly Test for Reg AZ Position x time t graph of an object is shown in the figure Ratio of speed of the particle at t 3 to that at t 7 second is x 10 O 33 5 519 O 10100

28 A body X is projected upwards with a velocity of 98 ms after 4 s a second body Y is also projected upwards with the same initial velocity Two bodies will meet after BCECE 2012 a 8 s e 12 s b 10 s d 14 s 1 26 G El

a 12 2 A police jeep is chasing with velocity of 45 kmh thief in another jeep moving with velocity 153 kmh Police fires a bullet with muzzle velocity of 180 ms The velocity with which it will strike the car of the thief is a 150 ms b 27 ms 1 EAMCET 2014 d 250 ms c 450 ms with constant acceleration along a entage

Two conductors have the same resistance at 0 C but their temperature coefficients of resistance are a and a The respective temperature coefficients of their series and parallel combinations are nearly AIEEE 2010 Oy y O 2 2 3 0 2 2 04 0 04 0 2 4 0 0 Medica 0

A particle moves in the X Y plane with a constant acceleration of 1 5 m s in the direction making an angle of 37 with the X axis At t 0 the particle is at the origin and its velocity is 8 0 m s along the X axis Find the velocity and the position of the particle at t 40 s Y 37 a 1 5 m s X

26 180 R 3 A particle is moving on a circular path of radius R as shown in the figure If it starts from point A then displacement of the particle after rotating through 780 is OR 2 OR Mark for Review Zero 02 21 hr min

d 250 s A train starts from a station A and covers a distance of 4 km to reach the next station B If the maximum possible acceleration of the train is 1 5 m s and its maximum retardation is 6 m s find the least time in which the train can 4 undertake the journey from A to B a 91 st b 71 s c 82 s d 75 s A mail train and a goods train are moving on the same track in the same direction with velocities 108 km hr respectively The driver of the mail train sights the 5

Shots are fired simultaneously from the top and bottom of a vertical cliff with elevation a 30 and 60 respectively and strikes the object simultaneously at the same point If a 30 3 m is the horizontal distance of the object from the cliff then the height of the cliff is K x 100 m Find the value of K h a 30 B 60 a 30 3 m

Velocity time equation of a particle moving in a straight line is V t 5t 6 m s The distance travelled by the particle in the time interval from t 0 to t 4 sec is in m O O O 71 3 06 16 3

The velocity of a body depends on time according to t 2 the equation v 20 The body is undergoing 10 a uniform acceleration c non uniform acceleration b uniform retardation d zero acceleration

train He is just able to get in Find the speed he is running on a 12 m s b 9 m s c 15 m s d 6 m s J E E 72 04 3 The maximum speed of a bus is 72 km hr It accelerates uniformly at the rate of 1 m s and retards uniformly at the rate 4 m s2 Find the least time in which it can do a journey of 1 km a 125 s 04 b b 62 5 s c 25 s A train starts from a station 4 and 22b a 01 R If the maximum possible d 250 s

A block of mass 1 kg slides down a curved track that is one quadrant of a circle of radius 1m as shown in figure m 1kg Its speed at the bottom is 2 m s The work done by the frictional force is O 8 J O 8J O 4 J 4J O R 1m

32 The water drops fall at regular intervals from a tap 5 m above the ground The third drop is leaving the tap at instant the first drop touches the ground How far above the ground is the second drop at that instant Take g 10 ms 3 75 m 2 4 00 m noo 4 2 50 m 81

12 A ball is thrown vertically downward with a veloci of 20 m s from the top of a tower It hits the groun after some time with a velocity of 80 m s TH height of the tower is g 10 m s 1 300 m 3 340 m Ans 1 2 360 m 4 320 m

br Suppose you are anchored near the shore of a channel in which there is steady current and you are going to run your motor boat with a constant v v speed of boat with respect to water to a dock directly across the channel on the opposite shore The way in which one might stee the boat to the dock is POINTING method In pointing method keep the nose of the boat pointed directly at the dock Velocity of boat with respect to water is v and velocity of water is u Width of water channel is b The time taken by boat to reach the dock is b current dock start pointing method

Three stones A B C are projected from surface of very long Inclined plane with equal speeds and different angles of projection as shown in figure The incline makes an angle 8 with horizontal if Ha Ha and He are maximum height attained by A B and C respectively above inclined plane then Neglect air friction A H Ho He C H H 2H B H H H D H H 2H 162

A cart on a roller coaster rolls down the track shown below As the cart rolls beyond the point shown what happens to the components of the velocity and acceleration in the direction cart 1 Velocity increases continuously acceleration first increases then decreases 2 Velocity first increases then decreases acceleration decreases continuously 3 Velocity first increases then decreases acceleration increases continuously 4 Velocity increases continuously

20 Q 4 1 A cart on a roller coaster rolls down the track shown below As the cart rolls beyond the point shown what happens to the components of the velocity and acceleration in the direction cart 1 Velocity increases continuously acceleration first increases then decreases 2 Velocity first increases then decreases acceleration decreases continuously 3 Velocity first increases then decreases acceleration increases continuously 4 Velocity increases continuously acceleration decreases continuously Two planes are flying at the same speed 200 m sec in opposite directions A machine gun mounted in one plane fired bullets at the other at right angles to their line of flight see figure How far apart approximately will the bullet holes made in the side of the second plane be if the machine gun fires 900 bullets per minute 3 1 13 m 2 27 m 3 39 m 4 54 m A particle of mass m enters a regi horizontally at time t 0 with speed midway between two plates that a separated by a distance h as shown in t figure The particle is acted on by bo gravity and by a time varying force th points upward and has magnitude F where b is a positive constant that sufficiently large such that the particle h the top plates without ever touching t bottom plate How long does it take for t particle to reach its lowest point Js 1 3 mg b 2mg b h 2 mg 2b 4 2mgb

1 From the graph of x versus t in figure can you tell whether there is an instant at which the acceleration is zero and velocity is non zero If so estimate t at this instant x m 20 10 0 1 2 t s 1 1 sec 2 2 sec 3 3 sec 4 4 sec 3 4

D 5 s An aeroplane is flying in a horizontal direction with a velocity 600 km hr and at a height 1960m When it is vertically below the point A on the ground a body is dropped from it The body strikes the ground at point B The distance AB equal to A 3 333km B 33 33km C 333 3km D 33 33m A particle is projected

A particle thrown up vertically reaches at half of the maximum height in 2 1 s The speed of projection of the particle is g 10 m s 1 5 2 m s 2 10 m s 3 40 m s 4 10 2 m s

A boat starts from rest from one end of a bank of river of width d flowing with velocity u The boat is steered with constant acceleration a in a direction perpendicular to the bank The point of start is origin direction of bank is x axis and perpendicular to bank is y axis The equation of trajectory of the boat is 1 y 3 y 2u ax u ax 2 y 4 y ax 2u au 2 X

Question 15 When a ball is vertically upwards at the maximum height The velocity is zero and therefore there is no acceleration acting on the particle The acceleration is present and therefore velocity is not zero The acceleration depends on the velocity as a dv dt is independent of the velocity The acceleration

16 A car moves with velocity v for time t and with velocity v for time t along a straight line The average velocity of car for duration t t will be 1 V V 2 3 2 2v V V V V V 1 1 17 An object travels 20 m in 10 s and further 5 m in V l V l 1 1 4 21 22

A particle experiences a constant acceleration for 5 second after starting from rest If it travels a distanc s in first 25 second and distance s in the next 25 sec then 2 5 1

Question Assertion A body can have acceleration even if its velocity is zero at that instant of time Reason The body will be momentarily at rest when it reverses its direction of motion If both Assertion and Reason are true and reason is the correct explanation of assertion If both assertion and reason are true and Reason is not correct explanation of assertion assertion is true but reason is false Both assertion and reason are false

Namaste an object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a hei ght 100 m What is the difference in their heights after 2 s if both the objects d rop with same accelerations How does the difference in heights vary wit h time

5 A particle moves from A to B through the path shown in figure The magnitude of displacement of the particle is A 10 m R 10 m K 20 m B 1 10 m 2 30 m 3 40 m 4 50 m 6 A car moves with velocity v for time t and with In as rea

Example Two infinitely long grounded metal plates again at y 0 and y a are connected at x b by metal strips maintained at a constant potential V a thin layer of insulator prevents then from shorting out Find the potential inside the rectangular pipe Va 22

A partici a way that its x coordinate varies with time according to the equation x 8 4t 6t The speed of the particle will vary with time as 3 2 1 XJ X 2 12

9 One night a man of height h 1 8 m is standing on the bank of a straight pond The water surface is calm on the opposite bank a lamp is at height H 5 4 m from surface of water Light emanated from the lamp appears as a flare bright spot after reflection from the water surface When the man starts walking along the bank the flare appears to him moving at constant speed u 3 ms relative to ground Find the speed in ms of the man

Choose the correct answer If magnitude of displacement of a particle is 10 m then the distance travelled by it can be 1 Equal to 10 m 2 Less than 10 m 3 Greater than 10 m 4 Both 1 and 3 rar starts from a point and reaches through 1

09 25 A particle starts from rest under constant acceleration a 4 m s Ratio of respective distance travelled by the particle in 3rd and 5th second of its motion is 05 9 Mark for Review 09 5 hr min

Suppose two children push horizontally but in exactly opposite directions on a third child in a sled The first child exerts a force of 79 N the second a force of 95 N kinetic friction is 7 5 N and the mass of the third child plus sled is 24 kg Using a coordinate system where the second child is pushing in the positive direction calculate the acceleration in m s

A car starts from a point P and reaches Q throu a path as shown in the figure If the car takes 1 to cover the journey then the average speed is 10 km P 10 km 10 km 1 5 km h 3 6 km h 10 km 10 km 2 10 km h 4 4 km h

A ball is dropped from a high rise platform at t 0 starting from rest After 6 seconds another ball is thrown downwards from the same platform with a speed v The two balls meet at t 18 s What is the value of v Take g 10 m s 1 60 m s 2 75 m s 3 55 m s 4 40 m s iformly from

9 7 A ball is dropped from a high rise platform at t 0 starting from rest After 6 seconds another ball is thrown downwards from the same platform with a speed v The two balls meet at t 18 s What is the value of v Take g 10 m s 1 60 m s AIPMT Prelims 2010 2 75 m s 4 40 m s ardin

18 A particle moving along x axis has acceleration f 1 160 1 7 where fo and T are T constants The particle at t 0 has zero velocity When f 0 the particle s velocity v is AIPMT Prelims 2007 2 fT at time t given f fo 1 1 T 16T2 0 4 f T

50 A particle moves along a straight line such that its displacement at any time t is given by t 61 3t 4 metres The velocity when the acceleration is zero is 1 3 m s 2 42 m s 3 9 m s 15 m s

14 A particle moves in a straight line with a constant acceleration It changes its velocity from 10 ms 1 to 20 ms 1 while passing through a distance 135 m in t second The value of t is 1 9 3 18 AIPMT Prelims 2008 2 10 4 12

c 7 A man takes 3 h to cover a certain distance along the flow and takes 6 h to cover the same distance opposite to flow In how much time he will cross this distance in still water b 4 h a 3 5 h c 4 5 h d 5 h ier 500 m wide is flowing at a rate of 4 m s A Al espect to

EX2 The average cross sectional area of a woman s femur is A 10 m and it is Lo 0 4 m long The woman weighs W 750 N Calculate the length change AL of this bone when it supports half of the weight of the woman N 2 1 3

Potential energy of a particle of mass 1 kg free to move x x 2 along x axis given as U mechanical energy of particle is 4 joule Assuming only conservative forces are acting on particle maximum speed of the particle is 2 ms 1 2 5 ms 1 3 ms 1 x joule Total 3 6 m s 1

A body A starts from rest with an accelertion a After 2 seconds another body B starts from rest with an acceleration a If they travel equal distances in the 5th second after start of A then the ratio a a is equal to 1 5 9 3 9 5 2 5 7 4 9 7