Kinematics Questions and Answers

A 300 m c 500 m C a 400 m B 23 Two bikers simultaneously start a race with constant speeds from point A to traverse a triangular track ABC one clockwise and the other in anticlockwise sense They simultaneously cross at B first time after a time interval At 4 min If they continue the race how long after they cross at B first time will they again simultaneously cross at B

1 10 20 10 the position of the other balls in metre height will be 2 15 20 15 3 5 51 20 4 5 10 20 A ball is dropped from a height of 20 m and rebounds with a velocity which is 3 4th of the velocity with which hits the ground What is the time interval between the first and second bounces g 10 m s d sec 2 4 sec 3 5 sec 4 6 sec A particle is thrown upwards from aro

Answer the following questions acceleration 1 Define 2 When is the acceleration of a body negative

24 On a straight section of a highway sensors are installed to measure traffic density For each lane of the highway a sensor runs on an overhead wire On a particular day a sensor running with a speed u 5 km h opposite to the flow of traffic underneath counts N 360 vehicles in a length L 1 km of the highway If all the vehicles are moving with the same constant speed v 40 km h and density of the vehicles is uniform calculate number of vehicles per l 100 m of the lane 05 A trai

A ray of light enters a spherical liquid drop refractive index 3 from air at an angle of incidence 0 0 it suffers two internal reflections not TIR inside the drop and finally comes out of the drop If 0 0 is such that the deviation of the ray with respect to its original direction is minimum find the value of 12 sin 0

A projectile can have the same range R for two angles of projection If t and to be the times of flights in the two cases then the product of the two time of flights is proportional to 1 R 3 1 R 2005 2 1 R 4 R ti 2usin 0 t2 2usin 90 9 2usin 90 9 2 tit 4 usine coset 2R 9 9

P is a point moving with constant speed 10 m s such that its velocity vector always maintains an angle 60 with line OP as shown in figure O is a fixed point in space The initial distance between O and P is 100 m After what time shall P reach O 1 10 sec 2 15 sec 100m 60 v 10m s 3 20 sec 4 20 3 sec

30 An object is dropped from rest Its velocity versus displacement graph is assume downward direction to be positive L 2 1 2 3 4 S S S

A car has to cover the distance 60 km If half of the total time it travels with speed 80 kmh and in rest half time its speed becomes 40 kmh 1 the average speed of car will be a 60 kmh 1 b 80kmh 1 c 120 kmh 1 d 180 kmh

A small ball thrown at an initial velocity u directed at an angle 0 37 above the horizontal collides inelastically e 1 4 with a vertical massive wall moving with a uniform horizontal velocity u 5 towards ball After collision with the wall the ball returns to the point from where it was thrown Neglect friction between ball and wall The time t from beginning of motion of the ball till the moment of its impact with the wall is tan37 3 4 3u 181 A B C 5g 5411 125g D 25g 5411 25g

The velocity time v t graph for a particle in straight line motion is given below The corresponding acceleration time a t graph will be a 1 O a 3 O t a 2 O a t t 4 O

the ball If yes what should be the angle A yes 60 B yes 30 C no D yes 45 The relation between time t and distance x is t ax bx where a and b are constants The acceleration is AIEEE 2005 A 2abv B 2bv C 2av D 2av it the rate of through a distance S then continues at constant speed for orced is 15 S then

A wheel of mass M rotating on a vertical plane can roll down an incline of inclination Prove that if a body of mass m is attached to its circumference the wheel will remain in equilibrium if sin m m M

48 The position vector of a particle varies with time as r ro 1 at t where ro is a constant vector a is a positive constant then the distance covered during the time interval in which particle returns to its initial position is V ro 1 2a1 a To a b To 2a c d ro 2 ro To a 200 C fut 120 sell 0 no 1 2at te be E 15 2 1 20 E so val Ay

20 An insect fly start from one corner of a cubical room and reaches at diagonally opposite corner The magnitude of displacement of the insect is 40 v3 ft Find the volume of cube a 64 3 ft b 1600 ft c 64000 ft d none of these 1 In above problem if the insect does not fly but crawls What is the minimum distance travelled by the insect a 89 44 ft c 40 ft b 95 44 ft d 80 ft

Example 14 A toy rocket of mass 0 1 kg has a small fuel of mass 0 02 kg which it burns out in 3 s Starting from rest on a horizontal smooth track it gets a speed of 20 ms after the fuel is burnt out What is the approximate thrust of the rocket What is the energy content per unit mass of the fuel Ignore the small mass variation of the rocket during fuel burning NCERT

84 From a point on the ground a particle is projected with initial velocity u such that its horizontal range is maximum The magnitude of average velocity during its ascent is 1 5u 2 2 5u 2 2 3 5u 2 2 4 u 5 85 The velocity of projectile at the point of projection is 21 31 m s The velocity at a point where the projectile reaches is 1 21 31 m s 2 21 31 m s

Example 3 70 An open lift is moving upwards with velocity 10 ms It has an upward acceleration of 2 ms 2 A ball is relative to ground projected upwards with velocity 20 ms Find 1 i time when ball again meets the lift ii displacement of lift and ball at that instant iii distance travelled by the ball upto that instant Take g 10 ms 2

ma 13 On an object of mass 1 kg moving along x axis with constant speed 8 m s a constant force 2 N is applied in positive y direction Find its speed after 4 seconds

If displacement of a particle is zero the distances covered 1 must be zero 2 may or may not be zero 3 cannot be zero 4 depends upon the particle

Two persons P and Q crosses the river starting from point A on one side to exactly opposite point B on the other bank of the river The person P crosses the river in the shortest path The person Q crosses the river in shortest time and walks back to point B Velocity of river is 3 kmph and speed of each boat is 5 kmph w r t river If the two persons reach the point B in the same time then the speed of walk of Q is 08 Imp

10 A body is dropped from the top of a tower at height 100 m Simultaneously another body is thrown up with a velocity 40 m s When and where they meet

Figure 3 24 gives the x t plot of a particle in one dimensional motion Three different equal intervals of time are shown In which interval is the average speed greatest and in which is it the least Give the sign of average velocity for each interval X 1 2

A particle moves along a circular arc of radius R making an angle of 0 at centre The magnitude of displacemen a 2R sin 0 2 b 2R sin 0 c R sin 0 2 d Rsine

45 A person travels the total distance in two parts in the ratio 2 1 with a constant speed of 30 km h in the first part and 40 km h in the second part What is the average speed of the journey

particle is projected with velocity 30 above on an inclined plane inclination of which from horizontal is 37 Choose propriate path air resistance is negligible U 30 37 b U 30 37 c u 30 37 d u 30 37

hematics All the graphs below are intended to represent the same motion One of them does it incorrectly Pick it up 1 2018 U ve 3 velocity distance L Slope 0 a ve time U 0 Uitve time 1 0 a ve 4 velocity Physics 3 position position time Parabola U tve a ve

ball is thrown at angle a 90 a 0 on inclined plane as shown in figure then the minimum speed of the ball during the otion is YA UK

A body is thrown vertically upwards Which one of the following graphs correctly represen2017 velocity vs time V 4 V f V U gt a ve edge of a cliff 240 m high with initial speed of time variation of

J A stone projected at angle 0 with horizontal from the roof of a tal building falls on the ground after three second Two second after the projection it was again at the level of projection Then the height of the building is 1 5 m 4 15 m 2 25 m 3 20 m

15 Two stones are projected from level ground Trajectories of two stones are shown in figure Both stones have same maximum heights above level ground as shown Let T and T be their time of flights and u and u be their speeds of projection respectively neglect air resistance Then COLT 2 3 l U U Yoordinale same for al 4

Example 9 4 Suppose while sitting in a parked car you notice a Jogger approaching towards you in the side view mirror of R 2 m If the jogger is running at a speed of 5 m s how fast the image of the Jogger appear to move when the jogger is a 39 m b 29 m c 19 m and d 9 m away Solution From the mirror equation Eq 9 7 we get fu u f For convex mirror since R 2 m 1 m Then 39 x1 39 39 1 40 for u 39 m U Since the jogger moves at a constant speed of 5 m s after 1 s the position of the image v for u 39 5 34 is 34 35 m The shift in the position of image in 1 s is 39 34 1365 1360 5 1 40 35 1400 1400 280 Therefore the average speed of the image when the jogger is between 39 m and 34 m from the mirror is 1 280 m s Similarly it can be seen that for u 29 m 19 m and 9 m the speed with which the image appears to move is 1 10 100 m m 1 150 Although the jogger has been moving with a constant speed the speed of his her image appears to increase substantially as he she moves closer to the mirror This phenomenon can be noticed by any person sitting in a stationary car or a bus In caso of simil 1 ms ms and ms respectively 60

straight line A particle is resting over a smooth horizontal floor At t 0 a horizontal force starts acting on t Magnitude of the force increases with time according to law F at where a is a positive constant and t is time For the figure shown which of the following statements is are incorrect a xt D 1 Curve 1 shows acceleration against time 3 Curve 2 shows velocity against acceleration 4 none of these dy fat dt 2 Curve 2 shows velocity against time Sav faxtd v xt 2 v kt lvplocity i i k What should be its acceleration so that it can

3 Three particles are projected upward with initial speeds 10m s 20m s and 30 m s The displacements covered by them in their last second of motion are x x and x then 1 4 9 X X 1 x x x 1 2 3 2 3 3 x x x 1 5 7 122 4 None of these 123 2 x x

A man is sitting inside a moving train and observes the objects outside of the train Then choose the single correct choice from the following statements all stationary objects outside the train will move with same velocity in opposite direction of the train with respect to the man 2 stationary objects near the train will move with greater velocity object far from train will move with lesser velocity with respect to the man angular velocity is diff velocity is same 3 large objects like moon or mountains will move with same velocity as that of the train 4 all of these

4 6 4 7 Velocity of a stone projected 2 second before it reaches the maximum height makes angle 53 with the horizontal then the velocity at highest point will be 1 20 m s 2 15 m s 3 25 m s 4 80 3 m s A stone projected at angle 0 with horizontal from the roof of a tal building falls on the ground after three

Speed of water in a river is 4 km h and man can swim at 5 km h Minimum time taken by the man to cross the river of width 200 m is 1 t h 2 h 25 1 15 h

sphere of mass M is attached to a massless spring of spring contant K It can roll without slipping along a horizontal surface If the system is released after an initial stretch the time period is 1 2 3 2 2M K 7M SV O mooooooo 4 2 2 5M 3K 4 2 3M 2K

The resultant of two vectors P and Q is R If Q is doubled then the new resultant vector is perpendicular to P Then R is equal to 2 Q 1 P Q 2PQ P 4 P Q P Q

8 A body is moving with uniform velocity of 8 ms When the body just crossed another body the second one starts and moves with uniform acceleration of 4 ms 2 The time after which two bodies meet will be a 2 s b 4 s c 6s d 8 s

3 Two cliff of heights 120m and 100 4m are separated by a horizontal distance of 16m I a car has to reach from the first cliff to the second the horizontal velocity of the ca should be 1 16 ms 1 3 2 ms 1 2 4 ms 1 4 8 mg 1

2 During the first 18 min of a 60 min trip a car has an average speed of 11 ms What should be the average speed for remaining 42 min so that car is having an average speed of 21 ms for the entire trip a 25 3 ms c 31 ms 1 b 29 2 ms 1 d 35 6 ms 1

Example 3 58 A man A moves due to East with velocity 6 ms 1 and another man B moves in N 30 E with 6 ms 1 Find the velocity of B w r t A

In the above problem if reaches the ground at a horizontal distance d the second ball reaches the ground at a horizontal distance 3 12 d 1 6d 2 3d 4 4d A ball is projected horizontally from the top of a building 19 6 m high If the line joining the point of projection to the point where it hits the ground makes an angle of 45 to the horizontal the initial velocity of the ball is 1 4 9 ms 1 2 9 8 ms 1 3 19 6 ms 1 4 14 7 ms

Illustration 8 A wire of resistance 0 5 m 1 is bent into a circle of radius 1 m The same wire is connected across a diameter AB as shown in figure The equivalent resistance is in ohms 1 T A C D 2 1 3 B TC 2 4 T 4

A car moving with a speed of 50 km h can be stopped by brakes after atleast 6 m If the same car is moving at a speed of 100 km h the minimum stopping distance is a 6 m c 18 m b 12 m d 24 m

63 For a projectile projected at an angle are equal tan 4 u sin 20 u sin 0 2g sin 20 g 1 tan A 4 tan 4 sin 0 2 D the maximum height and horizontal range 470 R Tant 34 H

A blind person after walking 10 steps in one direction each of length 80 cm turns randomly to the left or to right by 90 After walking a total of 40 steps the maximum displacement of the person from its starting point can be a zero c 16 2m b 8 2m d 32 m

5 A projectile is fired at some angle 0 with speed such that it crosses two walls of equal height symmetrically as shown The angle of projection with horizontal is Y vertically 1 53 3 45 t 2s 0 120 m t 6s X 2 37 4 60

of projection and B p a are projected simultaneously from the same point with the same speed but different angles A The line joining the positions of the particle at any subsequent time makes a constant angle with the horizontal 76 2 4 B The line joining the positions of the particle at any subsequent time makes a constant angle with the horizontal C The magnitude of the relative velocity of the first particle with respect to the second is 2u sin D The magnitude of the relative velocity of the first particle with respect to the co 2 2 2 a B 2 2 a B