Kinematics Questions and Answers

A lift is moving upwards with acceleration a A man in the lift drops a ball within the lift The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively 1 g g 3 g a q 2 g a g a 4 a g

18 Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string The string passes over a pulley which is frictionless see figure The acceleration of the system in terms of acceleration due to gravity g is 4 kg 1 2 3 g 2 g 5 g 10 6 kg

If the displacement of a particle x t 7 then 1 Velocity of the particle is inversely proportiona to t 2 Velocity of the particle is proportional to 12 3 Velocity of the particle is proportional to t HOS with constant accoloration

A particle starts from rests and travels a distance S with uniform acceleration then it travels a distance 2S with uniform speed finally it travels a distance 3S with uniform retardation and comes to rest If the complete motion of the particle is a straight line then the ratio of its average velocity to maximum velocity is

88 The monkey B shown in figure 5 E20 is holding on to the tail of the monkey A which is climbing up a rope The masses of the monkeys A and B are 5 kg and 2 kg respectively If A can tolerate a tension of 30 N in its tail what force should it apply on the rope in order to carry the monkey B with it Take g 10 m s 70N 100N B Figure 5 E20

If a If A 41 21 4k and B 41 2j ak are perpendicular to each other then find value of a If vector a 2b is perpendicular to vector 5 4b then find the angle between and b fA 21 2j k and B i 1 then b Find the projection of resultant vector of A and B on x a Find angle between A and B d the vector components of a 21 31 along the directions of 1

ig 3 14 Motion of an a Variation of acceleration with b Variation of velocity with time c Variation of distance with time Example 3 6 Galileo s law of odd numbers The distances traversed during equal intervals of time by a body falling from rest stand to one another in the same ratio as the odd numbers beginning with unity namely 1 3 5 7 Prove it swer Let us diri

2 15 A train starts from rest and moves with a constant acceleration of 2 0 m s for half a minute The brakes are then applied and the train comes to rest in one minute Find a the total distance moved by the train b the maximum speed attained by the train and c the position s of the train at half the maximum speed

The length breadth and thickness of a rectangular sheet of metal are 4 234 m 1 005 m and 2 01 cm respectively Give the area and volume of the sheet to correct significant figures

15 A particle starts with initial speed u and retardation a to come to rest in time T The time taken to cover first half of the total path travelled is 7 1 1 2 T 1 3 HIN T 2 2 4 3T 4

8 Two seconds after projection a projectile is travelling in a direction inclined at 30 to the horizontal and after one more second it is travelling horizontally The magnitude and direction of its initial velocity respectively are 1 2 20 m s 60 2 20 3 m s 60 3 6 40 m s 30 4 40 6 m s 30 MEDINA

D both A and B A particle is projected with a certain velocity at an angle 0 above the horizontal from the foot of a given plan inclined at an angle of 45 to the horizontal If the particle strike the plane normally then 0 equals A tan 1 3 B tan 1 2 C tan 1 2 D tan 3 A projectle is fired horizontally from an inclined plano of in ali

A particle moves along X axis whose velocity varies with time as shown in the figure Then which of the following graphs is are correct a b Displacement Time Time

33 Ball A is thrown up vertically with speed 10 m s At the same instant another ball B is released from rest at height h At time t the speed of A relative to Bis 2 10 2gt 1 10 m s 3 102 2gh 4 10 gt

51 A body starts accelerating uniformly from rest If t t and t3 are the time taken by the body to cover successive equal distances then t 3 is 1 1 2 3 3 1 2 3 2 1 2 1 3 2 4 None of these

A girl is riding on a flat car travelling with a constant velocity 10 ms1 as shown in the fig She wishes to throw a ball through a stationary hoop in such a manner that the ball will move horizontally as it passes through the hoop She throws the ball with an initial speed 136 ms with respect to car The horizontal distance in front of the hoop at which ball has to be thrown is P 1m B 2m 5m 10ms 1 C 4m D 16m

1 Which of the following velocity v time t curves cannot represent motion in one dimension 1 v 3 2 4 t

82 33 Find the mass M of the hanging block in figure 5 E16 which will prevent the smaller block from slipping over the triangular block All the surfaces are frictionless and the strings and the pulleys are light M 0 M

7 In the given figure three point charges are situated at the corners of an equilateral triangle of side 10 cm Calculate the resultant force on the charge at B What is its direction 2016 Two positively chargod portiolog 271 10 cm A 10 cm C q 100 C q 100 C 10 cm B q 100 C

Q1 System shown in the figure is released from rest g 10 m s Which of the following statements is are true B 2kg 30 1kg 2kg A Magnitude of acceleration of each block is 2 m s B Tension in the cord A is more than that in cord B C Tension in the cord A is less than that in cord B D Magnitude of difference in tensions in both the cords is 2 N

d None of these pendulum of mass m hangs from a suppo trolley The direction of the string f e a hen the trolley rolls up a plane of inclina ith acceleration a is A

A person moves 30m north and then 20m towards east and finally 30 2 m in south west direction The displacement of the person from the origin will be 1 10m along north 2 10 m along south 2 10m along west 4 zero

between A B is 1uF Find the value of C 1 C Ao H Bo 23 32 H UF 8 F 2 F 1 F HH 6 F 2 F 12 F I 4 F 32 23 HF 2

35 The v t plot of a moving object is shown in the figure The average velocity of the object during the first 10 s is 10 m s 0 10 m s 1 Zero v ms LO 5 LED 10 2 2 5 ms 1 t s

2 The heart of a man pumps 5 litres of blood through the arteries per minute at a pressure of 150 mm of mercury If the density of mercury be 13 6 10 kg m and g 10 m s then the power of heart in watt is Re AIPMT 2015 1 1 50 2 1 70

16 A particle is projected with a velocity u making a angle 0 with the horizontal At any instant its velocit v is at right angle to its initial velocity u then v is 1 u cos 0 2 u tan 0 3 cot A

The distance travelled by a body in the nth sec ond is given by the expression 2 3n Find the initial velocity and acceleration Also find its velocity at the end of 2 seconds

Atennis player X lofts the ball at 45 when his opponents 1 X He begins moving away from X later hoping to reach the ball and hit it back at the moment when its is at 3 6 m above its launch point Ignore the fact that he can stretch so that his racket can reach the ball before he does 15 0m s XQ 45 S 15m 3 13 Distance that Y must move before he can reach the ball is 18 m B 3 m C 15 m Minimum average speed must Y move with to hit the ball is 16 2 m s 15 2 17 m s T3 6m D 12 m D 2 2 m s

The mean value of urrent for half cycle for current variation shown by the graph is 1 3 10 2 O T NH 2 T 2 4 lo a 3T 2

ping distance F A 200 m long train starts from rest at t 0 with constant acceleration 4 cms 2 The head light of its engine is switched ON at t 60 s and its tail light is switched ON at t 120 s Find the distance between these two events for an observer standing on platform

beg silt noswisd noitoral inilison 26 Neglect friction Find accelerations of m 2m and 3m as shown in the figure The wedge is fixed 3m 2m m 30

2 44 Sample Problem 1 The displacement in metre of a particle moving along x axis is given by x 18t 5t Calculate i the instantaneous velocity at t 2 s ii average velocity between t 2 s Central School 2005 to t 3 s iii instantaneous acceleration 2

50 a due north b 30 east of north d 60 east of north c 30 north of west 13 In the arrangement shown in figure 3 Q3 the ends P and Q of an inextensible string move downwards with speed uniform speed u Pulleys A and B are fixed The mass M moves upwards with a b u cose c 2u cose a 2u cose d ucose OBJECTIVE II 1 Consider the motion of the tip of the minute hand of a plock In one hour It is zero PV Figure 3 Q3 Q 0 must 6 The velocity of a particle is zero at a The acceleration at t b The acceleration at t 0 may c If the acceleration is zero from in also zero in this interval

A ball is thrown upwards Its height varies with time as shown in figure If the acceleration due to gravit is 7 5 m s then the height h is Height m 1 10 m 3 20 m 1 2 hi 5 6 time s 2 15 m 4 25 m

10 kg rests on a horizontal table The A block of mass m coefficient of friction between the block and the table is 0 05 When hit by a bullet of mass 50 g moving with speed v that gets embedded in it the block moves and comes to stop after moving a distance of 2 m on the table If a freely V after being dropped 10 falling object were to acquire speed from height H then neglecting energy losses and taking g 10 m s the value of H is close to a 0 2 km b 0 3 km c 0 4 km d 0 5 km Online 2015

speed Two charge particles each of mass m carrying charge q and connected with each other by a massless inextensible string of length 2L are describing circular path in the plane of paper each with qB L where B is constant about their centre of mass in the region in which an uniform magnetic field exists into the plane of paper as shown in figure Neglect any effect of electrical gravitational forces m A 5 The magnitude of the magnetic field such that no tension is developed in the string will be Bo B B C 2B DLO

circumference C is at rest on the groun When the wheel rolls forward through half revolution then the displacement of point contact will be NEET 2016 76 A wheel of 1 TU 2 hestrated 4 3 4 2 1 2 2 4 TC 1

A particle is moving along a straight line Its displacement from a fixed point is given by s 6 t t Find a velocity when t 0 b time at which velocity is zero c distance travelled in the interval t 0 to t 2 sec 5

2n 2n 1 A body travels for 15 sec starting from rest with constant acceleration If it travels distance S S S3 in the first five seconds second five seconds and next five seconds respectively the relation bet S S and S is S S S3 2 5S 3S S3 3 S 1 3 4 S 5 1 5

projected vertically upward with speed u 10 m s During its journey air applies a force of 0 2v on the particle What is the maximum height attained by the particle m 2kg 1 5 ln 2 3 2 n 2 2 3 n 2 6 4 10 n 2

12 A particle starts from point A moves along a straight line path with an acceleration given by a p qx where p q are constants and x is distance from point A The particle stops at point B The maximum velocity of the particle is P b f c a w a 9 p d q 2 PRO

Two trains one of length 100 m and another of length 125 m are moving in mutually opposite directions along parallel lines meet each other each with speed 10 m s If their acceleration are 0 3 m s and 0 2 m s respectively then the time they take to pass each other will be 1 5 s 2 10 s 3 15 s 4 20 s

A man is running with constant speed of v 10 5 m s on a horizontal track of radius R 20 m as shown in figure At position A man launches a stone in space without changing his own speed so that he can catch stone at B diametrically opposite to A The speed of launch will be approximately 4K m sec Then find the value of K take 10 and g 10 m s A O B

49 The velocity v of a particle moving along x axis varies with its position x as shown in figure The acceleration a of the particle varies with position as v m s K 45 2 1 a x 2 2 a 2x 4 3 a x 2 4 a x 4 x m

The velocity of a particle moving in positive x axis is according to relation v 4x If at t 0 particle is at x 0 then the velocity and acceleration at t 2s are given as 1 4 m s 4 m s 2 2 m s 2 m s 3 2 m s 4 m s 4 4 m s 2 m s

0 In the figure given below the position time graph of a particle of mass 0 1 kg is shown The impulse at t 2 sec is I 2 1 0 2 kgms 1 2 0 2 kgms 3 0 1 kgms 4 0 4 kgms X m 6 4 2 220 011x2 4 2 t seconds 6

If block A shown in figure is moving with speed v as observed by a person on ground then the magnitude of velocity of A with respect to the block B is the wedge is fixed 1 v 3 v 3 30 A 2 2 4 Zero

A projectile is thrown from ground level with an initial velocity 41 3j It reaches its greatest height above ground level after A 0 2 s B 0 3 s C 0 4 s D 3 s

In the figure shown two boats start with different speed relative to water simultaneously Water flow speed is same for both the boats Mark the incorrect statements 0 and are angles from a y axis at which boats are heading at initial moment Flow A If v v then for reaching the other bank simultaneously 0 0 B In case A drift of boat A greater than boat B C If v v and 0 0 boat B reaches other bank earlier than boat A D If v v and 0 0 drift of A is less

TIPLE CHOICE A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and R Ro t where t stands for time The speed of the particle as a is equal to 1 rad s Distance of the particle from axis is given by function of time is A B 1 c B R Bt B R t D B