Kinematics Questions and Answers

5 For an object projected from ground with speed u horizontal range is two times the maximum height be attained by it The horizontal range of object is 067 UST 1 101 2u 3g 34 BIBA 2 3u 4g 4u

The minimum force required to start pushing a body up a rough frictional coefficient inclined plane is F while the minimum force needed to prevent it from sliding down is F2 If the inclined plane makes an angle 0 from the horizontal such that tan 0 2 then the ratio F F is 2012 73 3 1 2 4 4 2

1 2 a a 27 A particle is projected with a velocity 81 63 m s The time after which it will start moving perpendic to its initial direction of motion is 3 1 s 4 5 3 s 1 0 5 s 2 1 25 s 28 Consider the following statements A Linear momentum of a system of particles is zero PUIGGG

25 Let f R 1 be a function defined by f x x value of a is 26 Two objects moving along the same straight line are leaving point A with an acceleration a 2a and velocity 2u u respectively at time t 0 The distance moved by the object with respect to point A when one object overtakes the other is 1 2u 2 2 27 3u a A particla in pr od with a 4u 6u 3 4 a m s The time after which it will start moving perpendicular

A Ship A steams down north at a speed of 8 kmph and ship B due west at a speed of 6 kmph The velocity of A w r t B is 10 kmph Tan 2 10 kmph tan 3 10 kmph NE 4 2 kmph Tan 3 4 3 N of E E of N IN of E VA VB 36464

A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x 3t 4t t where x is in metres and is in seconds The work done during the first 4 seconds is a 5 28 J c 490 mJ b 450 mJ d 530 mJ

Example 8 Two blocks A and B are connected to each other by a string and a spring The string passes over a frictionless pulley as shown in Fig 6 46 Block B slides over the horizontal top surface of a stationary block C and the block A slides along the vertical side of C both with the same uniform speed The coefficient of friction between the surfaces of the blocks is 0 2 The force constant of the spring is 1960 Nm If the mass of block A is 2 kg calculate the mass of block B and the energy stored in the spring g 9 8 m s B Fig 6 46

Two particles P and P move towards origin O along X and Y axes at constant speeds u and u respectively as shown in the figure At t 0 the particles P and P are at distances a and b respectively from O Then the instantaneous distances between the two particles is given by the relation IJSO Stage 1 2018 P 11 A s a b u u 2t au bu 2 C s a b y 2t a bul12 1012 0 P2 B s a b u 2t bul taul

3 A bus is moving with a speed of 10 m s on a straight road A scooterist wishes to overtake the bus in 100 s If the bus is at a distance of 1 km from the scooterist with what speed should the scooterist chase the bus 1 10 m s 3 40 m s 2 20 m s 4 25 m s REDMI NOTE 5 PRO

23 A stone projected from ground with certain speed at an angle 0 with horizontal attains maximum height h When it is projected with same speed at an angle with vertical attains height h The horizontal range of projectile is 1 hy the 2 3 4 h h 2 2h h 4 h he 29 In

The friction of the air causes a vertical equal to 10 of the due to gravity Take retardation acceleration g 10m s The maximum height and time to reach the maximum height will be decreased by 1 9 9 00 100 2 11 11 10 00

For the acceleration time a t figure the change in velocity of particle from t 0 to t 6 sis a m s 4 1 10 m s 2 4 m s 3 12 m s 1 8 m s 2 4 6 xKxq t s 6 x 4

Hlaar Een a gel gel ula sit au d A del at ula 1 i udai THING AS Y ular s 60 H H 24 102m ludi on Y HEAH CuS m WRTH Hal Giul A

The ceiling of a long hall is 25 m high What is the maximum horizontal distance that a ball thrown with speed of 40 m s can go without hitting the ceiling of the hall g 10 m s

26 Two blocks connected by a spring rest on a smooth horizontal plane as m ooooo m F Shown in figure A constant force F starts acting on the block m a length of spring increases continuously if m m b blocks start performing S H M about centre of mass of the system with increasing amplitude c blocks start performing S H M about centre of mass of the system which with constant moves rectilinearly with acceleration d acceleration of m2 is maximum at initial

To lift a motor car from a ditch one end of a rope ABC is attached to a point A of a tree and the other end is tied at a point C of the car At the mid point B of the rope a pull of 200 kg wt is applied at right angles AC If ZABC 120 find the tension in the rope TAB al Camera

A tiger chases a deer 30 m ahead of it and gains 3m in first 5s after the chase started After 10s the distance between them is consider both at rest initially

Two projectiles are projected with velocity VA VB at angles 0 from horizontal and 0g from vertical as shown in the figure below such that VA VB but having same horizontal component of velocity Which of the following can not be correct y 1 TA TB 2 H HB 3 RA RB 4 RB RA OB 10 A VB X

32 The maximum height at which a small mass m can be placed on the parabolic bowl without slipping is s 0 5 Equation of parabolic bowl is y Where x and y are in metre y m x 10

1 Figure shows a projectile thrown with speed u 20 m s at an angle 30 with horizontal from the top of a building 40 m high Then the horizontal range of projectile is 0 40 m 1 20 3 m 2 40 3 m 3 40 m u 30

A car has a velocity of 40 km h After travelling towards east for 1 h it turns and moves towards north for 45 min It then turns towards east again and moves for 30 min Find the displacement of the car from its starting point 67 08 km 0 tan 1 north of east

A body released from rest from a certain height was observed to cover 78 4 m in the last two seconds before hitting the ground Find the height from which it was released g 9 8 m s 10 s 34 3 m Ans 123m hall

A particle moves with constant acceleration in the positive x axis At t 0 the particle is at origin and is at rest then correct graph between velocity and displacement is a c Displacement Displacement b d Displacement Displacement

A small particle slides from height H 45 cm as shown and then loops inside the vertical loop of radius R from where a section of angle 0 60 has been removed Find R in cm such that after losing contact at A and flying through the air the particle will reach at the point B Neglect friction everywhere A HA H B 60 R A VE H Vigh H

A wheel is rotating with angular velocity 2 rad s It is subjected to a uniform angular acceleratio a What angular velocity does the wheel acquire after 10 s b How many revolutions will it make in this time interval Sea

A wire of resistance 0 50m is bent into a circle of radius 1 m The same wire is connected across a diameter AB as shown in figure Find the equivalent resistance in ohms A C B

32 200 cal minute heat energy is supplied to a solid of 100 g The temperature of solid Q varies with time as shown The latent heat of fusion of the substance is Q 0 C Q Q 0 0 5 1 6 cal g 3 24 cal g 40 2 18 cal g 4 30 cal g 20 30 Minute

47 Two objects are moving in a straight line Their position x versus time t graphs are as in figure The relative velocity of A with respect to B is 1 sin 37 6553 m s 3 5 XA 53 B 137 A 2 t 3 4 m s

A lift starts ascending with an acceleration of 4 ft s At the same time a bolt falls from its ceiling 6ft above the floor Find the time taken by it to reach the ground g 32 ft s 1 2 1 0 S S 1 3 1 3 5 S 4 H S

5 A taxi leaves the station X for station Y every 10 minutes Simultaneously a taxi leaves the station Y als for station X every 10 minutes The taxis move at the same constant speed and go from X to Y or vice vers in 2 hours How many taxis coming from the other side will each taxi meet enroute from Y to X 2 11 4 23 1 10 3 12

A point which has velocities represented by 7 and 13 is at rest Find the angle between th direction of two smaller velocities 1 30 3 60 2 45 4 90

An object is thrown vertically upwards with a velocity of 60 m s After what time will it strike the ground use g 10 m s

in metres and time in seconds Draw x 1 time graphs for the following cases i x 3 5t ii x 2 The position of a particle as a function of time is given by

A ball is thrown vertically upwards with velocity of 30 m s If the acceleration due gravity is 10 m s2 what will be the distanc travelled by it in the last second of motic before again come to his hand A 5 m C 25 m B 10 m D 30 m

A train takes t sec to perform a journey if travel for t n sec with uniform acceleration then n 3 for t sec with uniform speed v and n finally it comes to rest with uniform retard ation Then average speed of train is 1 3n 2 3 3n 2 V V 3n V 2 2n 3 4 2n 3

A policeman starts chasing a thief with a uniform veloc ity V along a straight path in a jeep When the jeep is at a distance d from the thief the thief rides on a motor cycle and moves with a constant acceleration a start ing from rest Show that the policeman can catch the thief if V 2ad

Two particles A and B move with constant velocities V and V2 At the initial moment their position vectors are r and r2 respectively The condition for particles A and B for their collision is Re AIPMT 2015 1 7 72 V V2 2 r r2 V2 V1 2 V2 V

84 A point P is the contact point of a wheel on ground which rolls on ground without slipping The value of displacement of the point P wher wheel completes half of rotation If radius o wheel is 1 m 1 2 m 3 m 2 4 m 2 2 4 2 m T

A swimmer can swim at 3 2 km h 1 in still water He swims across a river when the velocity of current is 3 km h i In what direction should he swim to cross by the shortest path ii In what direction should he swim to cross the river in minimum time In that case how far will he be carried by the river current if the river is 2 km wide i 135 to the direction of current ii 90 to the direction of current 1 km

18 Draw a velocity versus time graph of a stone thrown vertically upwards and then coming downwards after attaining the maximum height

14 Some characteristics of velocity on time graph are shown on graphs below Which graph correctly represents the characteristics Velocity 0 Velocity 0 Displacement Displacement Velocity is increasing Velocity constant time t A Velocity 0 Velocity is decreasing Velocity is increasing time t C 1 Only A Displacement Displacement Velocity is constant Velocity is constant time t B Velocity is constant Velocity is increasing Velocity is zero time t D 2 Both B C B 21

A particle moves with uniform acceleration and V V and v3 denote the average velocities in three successive intervals of time t t2 and t3 Which of the following relation is correct 1 V V V2 V3 t t 1 13 2 V V V V3 t t 1 13 3 V V V2 V3 t t t 13

A particle crosses points A B C in a straight line at a constant acceleration The particle travels from A to B in time t and B to C in time t If AB a BC b then prove that the acceleration of the particle is 2 bt at t t t t

If F is the force acting on a particle having position vector F and be the torque of this force about the origin then 1 0 and F 0 2 F 0 and F 0 3 F 7 0 and F 0 4 F 0 and F 0

Two particles move near surface of earth with uniform acceleration g 10 m s towards the ground At the initial moment the particles were located at one point in space and moved with velocities v 3 0 m s and v 4 0 m s horizontally in opposite directions Find the distance V1 between the particles at the moment when their velocity vectors become mutually perpendicular

49 D particle is at the mean position the projectile is fired from the ground with velocity u at an angle 0 with the horizontal The projectile hits the oscillating particle Then the possible time period of the particle is A C u sin 0 g 2u sin 0 3g 2u sin 0 g D all the above B

A particle moves over the sides of an equilateral triangle of side with constant speed v as shown in figure Then X A The magnitude of average acceleration from A to C is v Neate B The magnitude of average velocity as it moves from A to C is N C The magnitude of average velocity as it moves from A to C is v 3 v 2 D The magnitude of average acceleration from A to C is 8 B C

A body is moving with constant acceleration a 5 m s from A to B in straight line AB The velocity of particle at A and B are 5 m s and 15 m s respectively The velocity at mid point of AB is 1 125 m s 2 250 m s 3 550 m s 4 600 m s

angles a and with the horizontal such that the maximum height of A is two third of the Two particles A and B are projected from the same point with the same speed but at different horizontal range of B Then which of the following relations are true A range of A maximum height of B B 3 1 cos 2 x 8 sin 2 B C maximum value of is sin 3 4 1 D maximum horizontal range of A u g and this occurs when sin 2 1 3 100

3 950 3 Which of the following option is correct about given graph y D C 7 B A 7 100004 X 1 A and B have minimum value of slope 2 B has minimum value of slope 3 D has maximum value of slope and have same value of slope