Kinematics Questions and Answers

If a ball is given a push so that it has an initial velocity of 5 m s down a certain inclined plane then the distance it has rolled after t seconds is given by the following equation s t 5t 2 a Find the velocity after 2 seconds m s b How long does it take for the velocity to reach 30 m s Round your answer to two

A bead can slide along a straight rod The friction coefficient between them is u At a certain moment t 0 the rod starts rotating about a perpendicular axis passing through its end At this moment the bead is at distance z from the rotation axis The space is free of gravity The angular velocity of the rod at any time t is co at where a is a positive constant The value of time t when the bead begins to move is A infinite B 4 a 2 3 D 2u a 3 C a 1 3

strokes normal to the river current How far down the river does he go when reaches the other bank 4 In a harbour wind is blowing at the speed of 72 km h and the flag on the mast of al anchored in the harbour flutters along the N E direction If the boat starts moving speed of 51 km h to the north what is the direction of the flag on the mast of the ba The ceiling of a long hall in 25 hisch w 1 die Tin

Ariver is flowing from west to east at a speed of 5 meters 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 A due north B 30 east of north C 30 north of west D 60 east of north

A particle is projected vertically upwards with velocity 20 m s at t 0 At what time particle is at height of 15 m and it is coming down g 10 m s Only One Correct Answer A B C 2 seconds 1 second C L i

ground with velocity 20 m s at an angle of 37 with horizontal Average velocity of the particle during the interval it lands on the ground is Only One Correct Answer A 12 m s B C 16 m s 6 m s i

A stone is dropped from top of a tower Choose the correct distance time graph for the motion of stone Only One Correct Answer B 9 D Time K K Time Distance Distance Distance Distance Time

In Fig M weights P and Q are suspended in a vertical plane by strings 1 2 3 arranged as shown in Fig M Find the tension induced in each string if P 30 kN Q 40 kN 40 and 50 Also find the inclination y of segment CD to the vertical Ans S 132 35 kN S 111 05 kN S 89 59 kN y 110 1 1 B P B 2 ir C Q 3 D

A U shape wire is formed by connecting a resistance R with two parallel conducting rod at its both ends and kept on a horizontal table A sliding wire PQ of length I and mass m can slide over the U Shape wire without friction This rod PQ is connected to a block of mass m through an insulating string going over a smooth pulley as shown A vertical magnetic field B is switched on and rod PQ is allowed to move from rest After some time it attains a constant velocity vo also called terminal velocity Now mass of the block is tripled it attain another terminal velocity VT Given B 10T 1 1 m vo 10 m s R 10 Q2 g Lung 777 The value of torminal volocity v ic 10 m s

A body has an initial velocity of 3 ms and has an acceleration of 1 ms2 normal to the direction of the initial velocity Then its velocity 4 s after the start is O O O O 7 ms along the direction of initial velocity 7 ms along the normal to the direction of initial velocity 7 ms midway between the two directions 5 ms at an angle tan 4 3 with the direction of initial velocity

1 Kinetic energy is being transformed into gravitational potential energy when a a stone is thrown vertically upward a ball is falling freely downward a car is accelerating downhill a train is brought to rest by application of the brakes e none of the above b c d

A brick is dropped from the roof of a house and it lands right before it reaches the ground with a speed v The speed right before it reaches the ground for an identical brick that is dropped from a roof twice as high as the first brick will be a 0 5v b v c 2v d 4v 1

eld at rest on part of the table If the ts end just 12 A ball is thrown onto a floor at an angle If its velocity vector is 41 3j m s and restitution then the velocity by which it coefficient is rebounds is 1 4 2 3 4 2 V 3 O y axis 2 41 2 4 41 3 EET A body of mass 1 kg travels in x axis NE A pa kine the 16

2 32 A block is given certain upward velocity along the incline of elevation a The time of ascent to upper point was found to be half the time of descent to initial point The co efficient of friction between block and incline is A 0 5 tan a 0 6 tan a B 0 3 tan a D 0 2 tan a

2 A conducting rod of length I falls vertically under gravity in a region of uniform magnetic field B The field vectors are inclined at an angle 0 with the horizontal as shown in figure If the instantaneous velocity of the rod is v the induce emf in the rod ab is a Bly b Blv cos 0 c Blv sin 0 d zero a V V

2 17 A block A kept on a rough plate 00 with coefficient of static friction 0 75 coefficient of kinetic friction p 0 5 The plate is leaning with horizontal at an angle tan If the plate is further tilted slightly then the acceleration of block will be A 1 5 m s 2 A Figure 2 143 0 B 2 m s D None of these

2 74 A pulley is attached to one arm of a balance and a string and The pulley is m passed around it carries two masses m provided with a clamp due to which m and m do not move On removing the clamp m and m start moving How much change in counter mass has to be made to restore balance m m m m C 2m m A m m l l Figure 2 174 m m m m B D m m

2 56 A man drags an m kg crate across a floor by pulling on a rope inclined at angle 0 above the horizontal If the coefficient of static friction between the floor and crate is u then the tension required in the rope to start the crate moving is A C mg sin 0 cos 0 H mg cos0 sin 0 B D Umg sin 0 cos 0 H mg cos 0 u sin 9 A C 2 6 truc the fric A C

g block 2 The s 0 60 ock is lting 2 39 A body of mass m starts sliding down an incline of 30 from rest The body comes to rest just when it reaches the bottom If the top half of the plane is perfectly smooth and the lower half is rough find the force of friction A mg 4 mg B D mg 3 mg 2

2 78 A horizontal rope of length y is pulled by a constant horizontal force F What is the tension at a distance x from the end where the force applied A C F y x y F y B D F y y x F y y

Q A particle of mass 2kg is projected with i nitial speed of 10 root 2m s at an angle of 4 5 degree from the ground find the change in momentum when the particle 1 is at maximum height 2 whon C

A stone is thrown from the top of a tower at an angle of 30 up with the horizontal with a velocity of 16 m s After 4 sec of flight it strikes the ground Let the height of tower is H meter Then the value H of is g 10 m s 12

Two boats moving in opposite directions in a river cross a float simultaneously Speed of both the boats is different with respect to water and remains constant After some time both the boats turned back simultaneously and return with same speed with respect to the water Which boat will reach the float first O O The boat with greater velocity with respect to the water The boat with lesser velocity with respect to the water Both the boats will reach simultaneously Data is insufficient

2 62 What should be the maximum value of M so that the 4 kg block does not slip over the 5 kg block Take g 10 m s 4 kg 0 4 5 kg A 12 kg C 10 kg smooth Figure 2 166 B 8 kg D 6 kg M

Both A B are thrown simultaneously as shown from a very high tower If distance between the two balls after 1 seconds is 10n in meter then value of n is Assume that the balls are thrown from the same point simultaneously BRAR ra af 1 gue are a a 10n HAI G A 3D Y THE KG HY J 1 10m s 1958 1000000 101000 10m s

An elevator of height h ascends with constant acceleration a When it crosses a platform bolt 2h drops from the top of the elevator If the time for the bolt to hit the floor of the elevator is Vg a then find 2

A point mass perform straight line motion along positive x axis At t 0 point mass is at A 5 0 It 9 moves such that its velocity is given by v where x is the x coordinate of position vector of point X mass at a certain time t Find the time required to move from A to B 13 0 in sec

A bifilar pendulum consists of a uniform rod suspended at its ends by two threads of equal length 1 as shown in Fig 1E 69 The system is displaced from equilibrium by rotating it through a small angle about a vertical axis passing through the midpoint C of the rod What is the angular frequency of oscillation of the system

Application 9 The height in metres of a flare as a function of time t in seconds since the flare was fired from a boat can be modeled by the function 5 25 t 4 86 a What is the maximum height of the flare b At what time does the flare reach its maximum height c What was the height of the flare when it was initially fired 1 mark 1 mark 2 marks

Vector V is 24 6 km h and points 16 2 north of east Vector 2 is 66 3 km h and points 35 2 east of south Determine the nagnitude and direction of VR e g 25 3 m s 88 degrees northwest or 25 3 m s 88 degrees north of west or 25 3 m s 88 degrees NW NB The examples provided serve as guide to answering format Beware of spaces and commas as this may affect your answer

4 23 A charged particle moves along a circle of radius r 100 mm in a uniform magnetic field with induction B 10 0mT Find its velocity and period of revolution if that particle is a A non relativistic proton b A relativistic electron Ans a 6 5 s b 4 1ns

A juggler maintains four balls in motion making each of the to rise of height of 40m from his hand what time inter should be maintain for the proper distance between them a 1 71 seconds b 2 14 seconds 1 41 seconds d 4 seconds

28 The ratio of the time taken to reach to top most point and to come back to earth by a body thrown vertically upward is a 1 1 b 1 2 c 2 1 d It depends of the mass of the body 29 The radius of gyration of a thin rod of length L about the perpendicular axis at its midpoin

An object at rest explodes into three pieces One piece has mass m and flies off along Another has mass 2m and flies off in the perpendicular direction along Mass m and mass 2m fly off with the same speed v The third has mass 3m Find the velocity u of the third mass immediately after the explosion

onstant acceleration of 3m s squared is located at 1 5 and has a velocity of v 1 10 What is the quation for the location as a function of time Part B What is the equation for the location as a function of time OA s t 2 75 7t 0 75t OB s t 3 5 7t 1 5t OC s t 5 10t 0 75t OD s t 5 10t 0 75t OE s t 5 10t 1 5t

A water clock clepsydra used in ancient Greece is designed as a vessel with a small orifice O figure The time is determined according to the level of the water in the vessel What should be equation corresponding to the shape of the vessel for the time scale to be uniform y y kx wherek 3 y kx where k 2 2 TV 2ga v 2 2 2 y kx where k 4 y kr whol 1 2ga 2 3 TV

6 A mass of 12 0 kg is placed on a table A string is tied to the mass and run over a pulley to a hanging mass If the coefficient of static friction between the mass on the table and the table is 0 342 what is the minimum value of the hanging mass that will start the system moving a 12 0 kg b 9 80 kg c 4 10 kg d 3 42 kg 7 A ball is suspended from the ceiling of a bus with a string as the bus moves at a constant velocity The driver applies the brakes and decelerates at a constant rate During this time a the tension in the string is zero b the tension in the string is equal in magnitude than the weight of the ball C the tension in the string is smaller in magnitude than the weight of the ball d the tension in the string is greater in magnitude than the weight of the ball 8 To be considered in uniform circular motion a body must do what move in a circular path maintain a constant speed a b c maintain a constant distance from a centre point all of the above 9 An airplane with a mass of 800 kg is flying in a circle of radius 500 m at 50 m s What is the centripetal force required to keep the airplane flying in the circle a 50 N b 80 N C 4000 N d 8000 N 10 Astronauts that spend long periods of time in free fall suffer from health effects including a muscles becoming larger b bones losing calcium C heart and blood vessels becoming smaller and constricted d kidneys processing less urine

c 1 3 24 The angle of projection of a projectile is 30 The ratio of the horizontal range and the maximum height is a 4 3 c 2 3 b 3 2 a 3 1 b 3 4 d 3 2 25 A person fires a bullet directly tow monkey sitting on a tree Just wh looves the gun the monke

Q1 Two stations A and B are 10 km apart in a straight track and a train starts from A and comes to rest at B For three quarters of the distance the train is uniformly accelerated and for the remainder distance uniformly retarded If it takes 15 minutes over the whole journey find its acceleration retardation and the maximum speed it attains 10 marks

6 A bomb is projected with a speed of 20 20 m s Before attaining its maximum height it explodes into two fragments of equal masses At the time of explosion projectile was going with speed of 25 m s f immediately after explosion one of the fragments moves horizontally while other moves vertically then 12 Separation between the points where two fragments lands on the ground is 20 7 m B Separation between the points where two fragments lands on ground is 20 5 m e Acceleration of COM of combined system till both the fragments lands on the ground is always equal to g D Acceleration of COM of combined system till the time both the fragments are in air is equal to g 12 20 10t S 204 1 101 2 IC so swt 10 no 4000 20x4

The mean velocity of blood flowing in a blood vessel of 2 mm internal diameter was measures in an experiment by means of a sensor which gave 1 V mm s The output was connected to a stig chart recorder whose y axis sensitivity was set at 20 mm V and waxis movement was set 100 mm minute If the length and area of the trace were 200 mm and 2800 mm respectively determine the velocity flow rate and total volume of blood that flowed in the said experiment o 2 57

31 What would the initial velocity of a ball have to be to reach a person that is 150 feet in the air if the ball is released from a point 6 feet off the ground Hint when the ball reaches its max height what is the velocity of the ball You will have to do a problem like this on the exam Vot 80 htt 16 2 Vot

Q A monkey of mass 20 kg descends down the rope whose breaking tension is 150N Find out minimum acceleration of monkey with which he can descend down without breaking the rope shant Sir

A block of mass m resting on a frictionless surface start moving under the influence of a constant force F The ratio of instantaneous power to average power developed by force F in time t is k 1 Find k

3 400 200 8 If the time of flight of a bullet over a horizontal range Ris T then the angle of projection with horizontal is 1 tan 97 2R 3 tan 2R g T h 2 tan 4 tan 2R gT 2R gT un in figure which quantity associate Lolong y axis

4 A projectile is given an initial velocity of 21 j ms where i is along the ground and j is along vertical If g 10ms the equation of its trajectory is 1 y x 5x 2 y 2x 5x 3 4y 2x 5x 4 4y 2x25x

An airplane is headed on a bearing of 174 at an airspeed of 250 km per hr A 59 km per hr wind is blowing from a direction of 233 Find the groundspeed and resulting bearing of the plane The groundspeed is km per hr Round to the nearest integer as needed The resulting bearing is Round to the nearest integer as needed

Find the distance travelled and di splacement of the body from t 0 to t 8 in the given acceleration ti me graph if at t 0 the body has a velocity of 10 m s a m s 2 0 2 4 6 2 4 8 t s

From a balloon moving upwards with a velocity of 12 ms a packet is released when it is at a height of 65 m from the ground The time taken by it to reach the ground is g 10 ms 2 a 5 s 4 s b 8 s 2017 c d 7 s

tring 4 B The een te F 2 9 A ball weighing 10 gm hits a hard surface vertically with a speed of 5 m s and rebounds with the same speed The ball remains in contact with the surface for 0 01 sec The average force exerted by the surface on the ball is BY 10N D 150N A 100N C IN