Kinematics Questions and Answers

12 Answer the following by appropriately matching the lists based on the information given in the paragraph A person has four cars a list of acceleration retardation according to cars is given below Acceleration m s Retardation m s Farrari Hondacity Alto K10 Nano 9 8 5 2 1 II Hondacity III Alto K10 IV Nano A IS II P III T IVU C IR II T III P IV Q A person starts from his home stop at Allen Distance between Allen his home is 2km along straight line path in minimum time If he choose car from list I then time to reach by him is given in list II List I List II Ferrari 1 2 P 40 sec Q 63 25 sec R 66 67 sec S 30 sec T 50 sec U 83 45 sec 5 2 B I P II T III R IV Q D IQ II P III T IVR

b A moving particle suffers elastic collision in one direction with another particle originally at rest having mass i x times ii 1 x times that of first particle Prove that the fraction of K E transferred from first to second ball is same in both the cases and obtain an expression for the fraction 3

A particle having a velocity v v at t 0 is decelerated at a rate of a B v where is a positive constant After What time does the particle come to rest 0 vo c t 2 a t b t d t 0 2 vo 4 V B

16 ALLEN fery A curved road of 50 m in radius is banked to 16 f 50m ferg correct angle for a given speed If the speed is to be doubled keeping the same banking angle the radius of curvature of the road should be changed to 1 200 m 2 100 m 3 50 m 4 none of these af ar dat groen f 1 200 m 2 100 m 3 50m 4 none of these

3 Answer the following questions in 30 40 words a Using the image given below explain the Newton s third law of motion 8 mark b A dog runs 100 m in 20 seconds He then comes back half the distance in seconds and stops What is the dog s average velocity c A body of mass 1 kg is kept at rest A constant force of 6 N starts acting on it Fi the time taken by the body to move through a distance of 12 m d Draw velocity time graphs to represent i an object travelling with uniform velocity ii an object travelling with uniform acceleration

SAMPLE PROBLEM 2 7 An alpha particle the nucleus of a helium atom travels along the inside of an evacuated straight tube 2 0 m long that forms part of a particle accelerator The alpha particle enters the tube at 0 moving at a velocity 9 5 X 105 m s and emerges from the other end at time t 8 0 x 10 s a If the particle s acceleration is constant what is the accelera tion b What is its velocity when it leaves the tube Solution a We choose the x axis to be along the tube with its positive direction to be that of the motion of the particle and we take the origin to be at the entrance of the tube so that x 0 We can find the acceleration by solving Eq 2 28 for a Data a y yo Voyt 1 2 a t y 0 x voxt Result x 2 0 m Vox 9 5 x10 m s t 8 0 x 10 s Substitute for x Vox and t and calculate a b To find the velocity as the particle leaves the tube we use Eq 2 26 Vx Vox axt Substitute for ax Vox and t and calculate v m s m s

4 A car travelling with a velocity of 80 km h slowed down 44 km h in 15 s The retardation is a 0 67 ms 2 b 1 ms 2 d 1 5 ms 2 5 An object is moving along the path OABO with constant speed then Dout B O c 1 25 ms 2 A a the acceleration of the object while moving along the path OABO is zero i If the mo taken as ii If the ob final ve iii If veloc then a decrea negati iv If vel v C b the acceleration of the object along the path OA and BO is zero c there must be some acceleration along the path AB d Both b and c up opp the v For we da po a

A horizontal force of value 0 1176 N acts on a block of mass 50 gm placed on the floor for a period of 5 s How fast did the block gain The variable friction coefficient between floor and block is 0 2

204 A man of mass M starts moving on a boat of mass M with constant velocity v with respect to the boat If the boat moves without any friction then the velocity of man with respect to ound is 1 V X3 M v M M 2 M v M M V 4 M M

15 a Suppose that a NASCAR race car is moving to the right with a constant velocity of 82 m s What is the average acceleration of the car b Twelve seconds later the car is halfway around the track and traveling in the opposite direction with the same speed What is the average acceleration of the car

GO For each of the three pairs of positions listed in the following table determine he magnitude and direction positive or negative of the displacement Initial position xo Final position x 2 0 m 6 0 m 3 0m a b c 6 0 m 2 0 m 7 0 m

Two bees A B were hovering in the garden near two flowers There positions with respect to origin are given for bee A 1 2 3 m and for bee B 3 2 1 m At t 0 they start moving towards each other with equal speeds and meet at a 1 point P If they meet at P after their speed must be 2 A 2m s B 2 m s C 2 2m s D 4 m s if you leave question unattem

A charged particles of energy 15eV moves through a perpendicular magnetic field The energy of the particle on emerging out of the magnetic field is A 15eV B 15eV C 15eV D may be more or less than 15eV depending on the sense of the applied field

in a region electric field of strength 2 kVm and a magnetic field of induction 0 5T are acting parallel to each other If a particle of charge 0 5mC and mass 1g enter that region with a velocity 10 m s parallel to the fields then its velocity after 1s in ms is A 103 B 2 x 10 C 3 x 10

the ground The third drop is leaving the tap the instant the first drop touches the ground How far above the ground is the second drop at that instant g 10 ms 2 A 1 25 m B 2 50 m C 3 75 m D 4 00 m

When a plane mirror is placed horizontally on level ground at a distance of 40 m from foot of a building the top of building and its image in the mirror subtends an angle of 90 at the eyes The height of building is 20 m 40 m 60 m 45 m 40 m

Izzy runs an 80 metre race in 14 seconds During the first 6 seconds her speed increases at a constant rate During the last 8 seconds her speed increases at a different constant rate Her speed at 14 seconds is 2 m s more than her speed at 6 seconds Here is a sketch of her speed time graph Speed m s 0 6 Time s Work out her acceleration during the last 8 seconds 14 Not drawn accurately

a 605 3 m b 53 A particle moves along a parabolic path y 9x constant and has a value 1 3 ms The acceleration of such a way that the x component of velocity remains 1 the particle is 1 2 ms a 3 b 3 ms 2 c 2 3 ms 2 d 2 ms oximum range 500 m If the 2 5

ime tas bt The particle starts from the origin with an initia velocity Vo The distance travelled by the particle in time t will be 1 vot b bt 1 3 Vot bt 1 Yot bt

6 A boy stretches a stone against the rubber tape of a catapult or gulel a device used to detach mangoes from the tree by boys in Indian villages through a distance of 24 cm before leaving it The tape returns to its normal position accelerating the stone over the stretched length The stone leaves the gulel with a speed 2 2 m s Assuming that the acceleration is constant while the stone was being pushed by the tape find its magnitude lorated 24 cm motion of the

Displacement r of a particle in x y plane varies with time t is given by r t i 21 m Velocity of particle at t 1 sis NCERT Pg 75 1 21 2j m s 3 41 m s 2 21 m s 4 42

A balloon is rising vertically upwards with uniform acceleration 15 7 m s A stone is dropped from it After 4sec another stone is dropped from it The distance between the two stones 6sec after the second stone is dropped in SI

45 The equation of projectile is Y 3x 9X The 2 velocity of projection is 2 ms 1 1 d 1 2 ms a 1 ms u 1 c 3 ms K 46 A ball of mass m is projected from the ground with an lo of A with the vertical

12 A cricket ball is hit for a six the bat at an angle of 45 to the horizontal with kinetic energy K At the highest point the kinetic energy of the ball is a zero b K K 2 d K 2

Q3 8 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 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

10 If a particle is moving along straight line with increasing speed then 1 Its acceleration is negative 2 Its acceleration may be decreasing 3 Its acceleration is positive 4 Roth 2 3

7 Two projectiles A and B are thrown from the same point with velocities v and v 2 respectively If B is thrown at an angle 45 with horizontal what is the inclination of A when their ranges are the same a sin 1 1 2 X2 sin b d sm sdt al 4 cool I 12 sin 1 1 12 5 sin 11 8 em 001 G 98

19 The initial velocity of a particle is u at t 0 and the acceleration a is given by af 2 Which of the following relations is valid 1 v u af 2 2 4 v u at5 15 2 5 3at 2 4 v u at5 2 2 v u

A projectile can have same range from two angles of projection with same initial speed If h and h be th maximum heights then a R h h c R 2 h h b R 2h h d R 4 h h

A car moves with speed 60 km h for 1 hour in east direction and with same speed for 30 min in south direction The displacement of car from initia position is 1 60 km 2 30 3 km 3 30 5 km

What is the relation between average speed and average velocity of body under its one dimensional motion Choose Your Answer Both are equal Average speed is greater than average velocity Average speed is less than average velocity Both are zero CLE

You ve told your friends and family that despite circumstances you are getting plenty of exercise by practicing basketball alone or with social distancing In actuality you are merely throwi wadded paper toward the trash can while binging Netflix The paper wad leaves your hand yo 2 12 meters above the floor traveling at an angle 8 16 4 degrees above the horizontal lands exactly in the middle of the track can Ytrash 1 03 meters high and Xtrash 3 16 meters away THROW Yo Vo 8 Calculate all the following The initial velocity vor of the paper wad The time it was in the air seconds Xtrash meters second Yurash

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion The stone remains in the air for mer 2 a Ga A 3 sec C 7 sec B 5 sec D 4 sec I at

From a tower of height h if two stones are thrown one upwards and the other downwards with the same velocity u and they reach the ground after t and t seconds respectively then which of the following is wrong 1 t t 2h g 2 t t 21 g 3 t t 21 g 4 h g t t

Assume that the cannon is fired at time t 0 and that the cannonball hits the ground at time f What is the position of the cannonball at the time 1 2 Answer numerically in units of meters View Available Hint s VAX4 E

24 A body of mass m is thrown upwards at an angle with the horizontal with velocity v While rising up the velocity of the mass after t seconds will be v cos 0 v sin 0 2 a 2 RA b v cos 8 v sin 0 gt 2 2 2 2 2 9 4 2v sin 0 gt d g t 2v cos 0 gr gt initial relocity of with Ava 34

A particle is thrown vertically upwards from ground Its velocity at half of the maximum height is 10 ms Then total time of flight of this particle is g 10 m s 1 1 sec 2 2 sec 3 2 sec 4 2 2 sec

velocity 3v What is the height of the tower A motorcyclist moving with uniform retardation takes 10 s and 20 s to travel successive quarter kilometer How much further he will travel before coming to rest A stone is thrown vertically unwards with a velocity of 19 6 m s After 2 second another stone 115

2 A river is flowing from west to east at a speed of 5 metres per minute A man on the south bank of the river capable of swimming at 10 metres per minute in still water wants to swim across the river in the shortest time He should swim in a direction

14 Which of the following option is correct about given graph 0 00 0 1 A and B have minimum value of slope 2 B has minimum value of slope 3 D has maximum value of slope 4 A B C and D have same value of slope

0 For a given velocity a projectile has the same range R for two angles of projection If t and t2 are the time of flight in the two cases then t t is equal to R 4R 2R b d c v a 29 g 9 od b R 9

A body is projected with velocity 20 m s making an angle 531 with the horizontal Among the following the time after which its vertical component of velocity is equal to the horizontal component is g 10 m s 0 2 S O1s 0 6 s

A ball is thrown from the ground with a velocity of 20 m s making an angle of 30 with the horizontal The ball will be at a height of 5 m from the ground after a time t equal to g 10 ms 1 2 sec 2 3 sec 3 1 sec 4 3 sec

A ball is released from the top of a tower of height 40 metre It takes T second to reach the ground What T is the position of the ball in in second 1 10 m from the ground 2 20 m from the ground 3 30 m from the ground 4 40 m from the ground

Figure shows the position time graph for a particle in one dimensional motion What is the displacement of particle in first 4 seconds x m 10 5 2 5 m 5m zero 15 m 8 t s Marks 4 1

3 1 2 mgl 4 2mgl 23 A ball is thrown vertically downwards with velocity 23 h 2gh from a height h After colliding with the ground it just reaches the starting point Coefficient of restitution is 1 1 2 3 1 2 1 2 4 2 gd 1 mv 3 1 2 mgl uftk f fa 1 1 2 3 1 Space for Rough Work C erdei

6 E A nh Vo 8 2V 0 V B A particle of mass m is moving in a circular orbit Its potential energy is U A Br where A and B are positive constants and r is the radius of the orbit If Bohr s quantum condition holds here find a Maximum possible de Broglie wavelength associated with the particle b The total energy of the particle in terms of the quantum number n man ne nan 1 2 This 2 c a filled with a visCONS

A particle of mass 1 kg moves in a straight line under the influence of a force which increases linearly with time at the rate of 60 N s it being 40 N initially Determine the position velocity and acceleration of the particle after a lapse of 5 s if it started from rest at the origin

1 Cheetahs can reach a top speed of 34 m s about 76 mph Suppose a stretch of land in the savanna is 130 m long If a cheetah reaches its top speed starting at rest within that entire stretch what is the rate of acceleration Assume acceleration is constant and the cheetah is running in a straight line towards some unsuspecting prey 10 points

3 You are on top on the school building with a snowball You see your favorite Physics teacher walking by about 120 m away from you How fast must you throw the snow ball to hit her assume you hit her on the foot and you throw the snow ball horizontally from a height of 13 5 m