Kinematics Questions and Answers

5 10 Two particles are moving along a straight line as shown The velocity of approach between A and B in V A 1 V V 2 IV V l 3 VA VB Lorvo va VA A man who can swim at the rate of 2 km hr in still river crosses a river to a point exactly opposite

A particle P is projected from a point on the surface of smooth inclined plane see figure Simultaneously another particle Q is released on the smooth inclined plane from the same position P and Q collide after t 4 second The speed of projection of Pis 1 5 m s 2 10 m s 60 3 15 m s 4 20 m s

The acceleration a of a particle moving in a straight line varies with velocity v as a 1 v m s2 where v is in m s If initially the particle was at rest then 1 Maximum velocity of the particle will be 1 m s 2 Maximum acceleration is 1 m s 3 The particle will finally come to rest 1 4 Velocity of particle at t In2 s is m s

Consider a disc rotating in the horizontal plane with a constant angular speed about its centre O The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure When the disc is in the orientation as shown two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y z plane an same for both pebbles with respect to the disc Assume that i they land back on the disc before 1 o the disc has completed rotation ii their range is less than half the disc radius and iii 8 2012 remains constant throughout Then A P lands in the shaded region and Q in the unshaded region B P lands in the unshaded region and Q in the shaded region C Both P and Q land in the unshaded region D Both P and Q land in the shaded region X Q

4 9 A particle is projected with speed 10 m s at angle 60 with the horizontal Then the time after which its speed becomes half of initial 1 11 13 sec 2 1 sec 3 3 2 sec 4 3 2 sec

A particle is projected on an incline of inclination 45 as shown in the given figure Acceleration of the particle at its highest point is pent meday 1 g 3 0 48 77777 30 45 Ground 2 2 4 3g

1 A car moving with a speed of 40 km h can be stopped by applying brakes after at least 2m If the same car is moving with a speed of 80 km h what is the minimum stopping distance 4 8 m

1 Horizontal drift of the balloon when angle of elevation acquires its maximum value is closest to a 180 m c 300 m b 200 m d Insufficient information 140 V 14 Questions 32 to 35 are based on the following physical situation Two particle A and B are moving towards each other on a straight line with equal speeds 5 m s At an instant that is assumed t 0 s distance between the particles is 100 m It is desired to move another particle C always maintaining a distance 40 m from the particle A and 30 m from the particle B When and for how long can the particle C fulfil the given condition a 3 s t 9 s b 9 s t 11 s 8 4 d 3 s t 17 s c 11 s t 17 s Cot the instant t 5 s

AKITEBYLCTERarts from rest and travels with an acceleration of 5m s2 what will be the velocity after 3 s

moving along x axis is as shown in figure 3 a O The corresponding position time x t graph of the particle may be represented by X K nam t 2 K t 4

23 The radius of circle the period of revolution initial position and sense of revolution are indicated in the fig 2 y t 4 sin 3 y t 3 cos IP 0 y projection of the radius vector of rotating particle P is 1 y t 3cos2nt where y in m rt 2 3 t 2 3m 9 T 4s where y in m 2 where y in m rt 4 y t 3 cos where y in m 2 NEET UG 2019 Odisha The distance covered by a particle undergoing SH in one time period is amplitude A 1 zero 2 A 3 2A 4 4A A mass falls from a height h and its time of fa is recorded in terms of time period T of a sim

36 A car starts from rest and moves with constan acceleration on a straight road The ratio o displacement travelled by car in first 4 seconds and next 4 seconds 1 1 2 3 1 3 2 1 1 4 1 4

4 3 5s A car starting from rest and moving with uniform accelera possesses average velocities 5 ms 10 ms the first second and third seconds What is the total dista covered by the car in these three seconds 1 and 15ms 1 15m 3 55m A ball is dropped from the top of the town covers a distance of h 2 in the l long does the hall 2 30m 4 None of these

The origin by a for where k is a constant and Y is the distance of the electe Suppose an electron is al k from the origin By applying Bohr model to this system the radius of the n orbital of the electron is found to be t and the kinetic energy of the electron to be T Then which of the AIEEE 2008 AMU Med 2010 following is true a T independent of n r n 1 b T n Ton c T r n n d Tt cn

6 A block A of mass m is tied to a fixed point C on a horizontal table through a string passing round a massless smooth pulley B figure 5 W5 A force F is applied by the experimenter to the pulley Show that if the pulley is displaced by a distance x the block will be displaced by 2x Find the acceleration of the block and the pulley Inups C A m ni B F als006 als bedwawob

Derive an equation for path of a projectile fired at an angle from the ground

4 A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds What should be the speed of the throw so that more than two balls are in the sky at any time Given g 9 8 m s a more than 19 6 m s b at least 9 8 m s c any speed less than 19 6 m s d only with

A particle is thrown obliquely at t 0 The particle has same K E at t 5 second and at t 9 second The particle attains maximum altitude at 1 1 6 s 2 4778 3 1 8 s 4 f 14 s A particle of mass m is thrown at t 0 with kine ongle 30 with the horizontal fro

A particle at rest falls under gravity g 9 8 m s such that it travels 53 9 m in last second of its journey Total time of fall is 1 4 s 3 6s 2 5s 4 7s

A man crosses a river in a boat If he crosses the river in minimum time he takes 10 minutes with a drift 120m If he crosses the river taking shortest path he takes 12 5 minute find i width of the river ii velocity of the boat with respect to water iii speed of the current Assume Vblr V

with the horizontal smooth plane as shown hits a small ridge at O The angular block after it hits O assuming it does 2 4 Zero imited 3v 2a P 24 A uniform solid cylinder of radius R is spun and then placed on an incline having coefficient of friction tane 0 is the angle of incline The cylinder continues to spin wihout falling for time 1 4 3 Ro 3gsin0 Ro 2 2gsine Ro gsine 2R000 gsin0 0

The graph between displacement and time for a particle moving with uniform acceleration is a a straight line with a positive slope b parabola c ellipse straight line parallel to time axis

A boy walks uniformally along the sides of a rectangular park of size 400 m 300 m starting from one corner to the other corner diagonally opposite Which of the following statement is incorrect 1 He has traveled a distance of 700 m 2 His displacement is 700 m 3 His displacement is 500 m 4 His velocity is not uniform throughout the

is 30 A table with smooth horizontal surface is placed in a cabin which moves in a circle of a large radius R figure 7 E5 A smooth pulley of small radius fastened to the table Two masses m and 2m placed on the table are connected through a string going over the pulley Initially the masses are held by a person with the strings along the outward radius and then the system is released from rest with respect to the cabin Find the magnitude of the initial acceleration of the masses as seen from the cabin and the tension in the string 0 m

Choose the Correct Answer A particle starts from rest with constant acceleration and its velocity after t second is v The displacement of the particle in last two second of its motion is equal to 1 t 1 2 2 t 1 y 0 4 2 1 2 d 3 2 t 1 IC

A 14cm C 0cm B 7cm A person crosses a 600m long street in 5 minutes The speed of the person in kr is A 7 B 7 2 C 2 D 4

2 A very broad elevator is going up vertically with a constant acceleration of 2m s2 At instant when its velocity is 4 m s a ball is projected from the floor of the lift with speed of 4 m s relative to the floor at an elevation of 30 The time taken by the ball to return the floor is 1 S 1 3 S 2 Im 3 S 4 1s

39 If velocity of a particle moving in a straight line given by v 2t 3 where t in sec and v in m s Then its average velocity in the interval 0 ts is 1 1 m s 3 3 m s 2 5 m s 4 4 m s

A piece of ice slides down a 45 incline in twice the time it takes to slide down a frictionless 45 incline What is the coefficient of friction between the ice and incline a 0 25 c 0 75 b 0 50 d 0 40

70 Two particles P and Q simultaneously start moving from point A with velocities 15 ms and 20 ms respectively The two particles move with accelerations equal in magnitude but opposite in direction When P overtakes Q at B then its velocity is 30 ms The velocity of Q at point B will be a 30 ms b 5 ms 1 d 15 ms 1 c 20 ms

The velocity time relation of an electron starting from rest is given by u kt where k 2 m s The distance traversed in 3 sec is

KINEMAT 48 A particle moves with a velocity v in a horizontal circular path The change in its velocity for covering 60 will t 1 v 2 4 v 2 v 2 3 v 3

Two particles A B are projected from a building A is projected with speed 2V making an angle 30 with horizontal B with speed V making an angle 60 with horizontal Which particle will hit the ground earlier v B 60 2V A 430 lale h 1 Particle A 2 Particle B 3 Particle A B will hit at same time 4 None of these A

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

A knife of mass m is at a height from a large wooden block The knife is allowed to fall freely strikes the block and comes to rest after penetrating distance y The work done by the wooden block to stop the knife is 2 mgy 4 mg x y 1 mgx 3 mg x y

34 Two paper screens A and B are separated by distance 100 m A bullet penetrates A and B at points P and Q respectively where Q is 10 cm below P If bullet is travelling horizontally at the time of hitting A the velocity of bullet at A is nearly 1 100 m s 3 600 m s 2 200 m s 4 700 m s

A uniform rope of mass 2 kg which can tolrate maximum tension 80 N at any point find maximum value of F which can be applied on 2 kg block A 112 N B 80 N C 180 N D 126 N 44 2kg 2kg 3kg

0 A body is released from a height and falls freely towards ground Exactly 1 sec later another body is released What is the distance between the two bodies 2sec after the release of the second body if g 9 8m s2 and no body has reached ground by then i o 1 45m 3 25m 2 44 3m 4 24 5m

5 The driver of a car moving towards a rocket launching pad with a speed of 6 m s observed that the rocket is moving with speed of 10 m s The upward speed of the rocket as seen by the stationary observer is nearly a 4 ms 1 c 8 ms 1 b d 6ms 1 11ms 1

A proton of mass m and charge e is projected from a very large distance towards an a particle with velocity v Initially a particle is at rest but it is free to move If gravity is neglected then the minimum separation along the straight line of their motion will be 1 4 mv 3 2e 4 mv 2 5e 4 mv 4 4e 4 mv

Problem 4 35 Ship A is 10km due west of ship B Ship ship B is heading in a direction 60 west of north at a A is heading directly north at a speed of 30 kmph while speed 20kmph Their closest distance of approach will

2 3 45 2 The velocity of water in a river is 2 kmph while width is 400 m A boat is rowed from a point rowing always aiming opposite point at 8 kmph of still water velocity On reaching the opposite bank the drift obtained is 1 93 m 2 100 8m 3 112 4 m 4 100 m A person swims at 135 to current of river to

38 Starting from rest the acceleration of a particle is a 2 t 1 The velocity of the particle at t 5 s is

The velocity time graph of a body moving along a straight line is as follows The displacement of the body in 5 sec is 1 5m 2m s 1m s 2m s 1 2 3 4 5 2 2m

A car accelerates on horizontal road Its position time graph is shown in the figure Find the average speed of the car from t 0s to t 60s 131 x m A 1 m s B 35 05 m s C t sec 10 60 m s D 7 12 m

Two cars are moving in the same direction with a speed of 30 km h They are separated from each other by 5 km Third car moving in the opposite direction meets the two cars after an interval of 4 minutes The speed of the third car is 1 30 km h 2 25 km h 3 40 km h 4 45 km h

Consider two infinitely long parallel uniformly charged non conducting wires with linear charged density 22 as shown A charge hangs in equilibrium by means of an insulating chargeless thread between the wires The mass of the charge is 1 3 1 JEE Foundations Educational 40 q 9 olg 160 q gravity 1 1 22 q m 2 4 42q 9 olg 40 q

If the velocity of a particle is v At Bt where A and B are constants then the distance travelled by it between 1 s and 2 s is 3 a 7 A B 3 2 3 c A 4B 2 NO b A B olcom 2 3 d 3A 7B 131 bit A

A charged sphere of mass m and charge q starts sliding from rest on a vertical fixed circular track of radius R from the position as shown in figure There exists a uniform and constant horizontal magnetic field of induction B Find the maximum force exerted by the track on the sphere G m 4313 0 R E OB

5 A boat covers certain distance between two spots in a river taking t hrs going downstream and t hrs going upstream What time will be taken by boat to cover same distance in still water 2 2 t 1 3 t t 2 2t t2 t t 4 t t2 words North