Kinematics Questions and Answers

A small body is thrown at an angle to the horizontal with the initial velocity vo Neglecting the air drag find a the displacement of the body as a function of time r t b the mean velocity vector v averaged over the first t seconds and over the total time of motion

8 A small body is thrown at an angle to the horizontal with the initial velocity vo Neglecting the air drag find a the displacement of the body as a function of time r t b the mean velocity vector v averaged over the first t seconds and over the total time of motion

Two blocks of mass 20 kg and 10 kg are connected by a massless string as shown in the figure How much time will 20 kg block take to travel 0 6 m distance when released from rest Take gravitational acceleration as 10 m s 1 0 2 s 10 kg 20 kg 2 0 4 s

body is projected from ground at speed v at an angle above horizontal Radius of curvature of its path at the highest point is 1 2 3 v cos e 2g V cose g v cos 0 g

4 30 km 221 A particle is moving along a straight line its position varies x 6a t asin ba t a sin where x is its position 1 t a 2 with time t as metre t is time in s and a is a positive constant The particle comes to rest at T 2 t a 3 t n 4 t 0 in d en ont ats si

42 If a particle loses 20 of its speed after penetrating through a single plank Calculate the minimum number of planks required to completely stop the plank 1 6 3 4 2 8 4 3

3 A particle is thrown with a velocity of u m s It passes A and B as shown in figure at time t 1 s and t 3 s The value of u is g 10 m s AY U 30 O 1 20 m s 3 40 m s A B 2 10 m s 4 5 m s

From the concept of directed dimension what is the formula for a range R of a cannon ball when it is fired with vertical velocity component Vy and a horizontal velocity component V assuming it is fired on a flat surface Range also depends upon acceleration due to gravity g and k is numerical constant R R k VzV 9 k V 9 k V Vg 3 k V Vz9

The horizontal position of a car in kilometres over time is shown below Position Kilometres 160 120 80 40 80 10 Time hours a Find the displacement and the distance travelled by car between 1 hour and 3 hours Ans Okm Okm b What is the displacement and distance covered by the car between 3 hours and 5 hours Ans 120km 120km c Calculate the displacement and the distance travelled by car between 5 hours and 9 hours Ans 160km 160km d Find the displacement and the distance covered by the car

8 A projectile is projected at some angle from the ground towards east in the absence of air resistance then time period and range of projectile are T and R If wind starts blowing towards east with some acceleration then the new time period T and range R have the relations 1 T T and R R 2 T T and R R 3 T T and R R A T I and R S P

the correct statement s regarding the motion of a particle A If instantaneous velocity of a particle is zero then its instantaneous acceleration wil necessarily be zero B If instantaneous velocity of a particle is zero then it can have instantaneous acceleration C A situation is possible in which instantaneous velocity of a particle is never zero but average velocity in that interval is zero D A situation is possible in which the speed of a particle is never zero but average speed in that interval is zero

Two identical springs of force constant k are connected 1 in series 2 in parallel and support a mass m The ratio of the period of oscillations of the series arrangement with that of the parallel arrangement is Question Type Single Correct Type 1 2 3 1 1 1 2 1 4

A force of 20N acts on 16 kg block kept on a smooth horizontal surface for 6 se and then removed Find the distance covered by it in 10 s a 52 5m b 62 5m c 42 5 d 32 5

A block of mass 4 kg is moving with a velocity of 12 m s on a horizontal smooth surface A force of 6N started acting on the block in the opposite direction of velocity After what time from the instant the force comes in to action the distance covered is equal to 2 5 times the displacement and what the velocity is then a 13 2sec 7 8m s c 11sec 5 8m s b 12sec 8m s d 26 4ec 7 8m s

If X is the total tension for all the strings of the given pulley what is the S I unit value of X 20 TA AT TA AT TA AT 60 Kg If X is the total tension for all strings of give

A force of 30 N acted on a block of mass 12 kg at rest for 6 sec and then the direction of the force is reversed a What distance the block moves before coming to rest b After what time the block reaches the starting point and with what velocity a 80 m 6 2 2 sec 15m s c 70 m 6 2 2 sec 15m s b 45 m 6 2 2 sec 15m s d 40 m 6 2 2 sec 15m s

Three particles P Q and R are situated at corners of an equilateral triangle of side length d At t 0 they started to move such that P is moving towards Q Q is moving towards R and R is moving towards P at every instant After how much time in second will they meet each other a DU P 62d 3u u R 2d 3 u c d d 3 u

Q Katrina and Kareena were crossing a river which is flowing towards right at constant speed 5m min travelling in two different boats having same speed in still water They have taken photographs of the river banks at t 0 t T t 2T times Bo Co are two trees on other bank of river Distance shown in diagram are in m Photograph taken by Katrina B Bo t 0 15 3 15 3 13 10 30 Photograph taken by Kareena 1 0 0 B t T c 10 3 Bol t 2TC 5 5 19 5 3 2T T 1 min Mark the correct option A Velocity of boat in still water will be 10 m min B Velocity of boat in still water will be 10 3 m min C Velocity of boat in still water will be 10 3 m min D Valoite of heat in still ill be 5 12 malmin

2 21 23 Ne decays to 23Na by negative beta emission Mass of 23 Ne is 22 994465 amu mass of 23Na is 22 989768 amu The maximum kinetic energy of emitted electrons neglecting the kinetic energy of recoiling product nucleus is MeV

The speed time graph of a car is given here Using the data in the graph calculate the total distance covered by the car a 1250 m 30 b 875 m c 1500 m d 870 m 25 20 speed in m s 10 5 15 0 A B 10 20 time in s C D E 30 40 G H 50 5

Two particles are projected from position A and B seperated by a distance of 80 m on horizontal ground If both the particles collides in mid air Select the correct statement Both particles are projected simultaneously A They will collide if angle of projection for A is 37 B Particles will collide somewhere between the two points A and B for any value of 0 C Particles will collide at t 1 sec after projection D They will collide if angle of projection for A is 53 40 2 m s 50m s

A child drops a toy at rest from a point 3 0 m above the ground at the same instant her friend throws a ball upward at 6 8 m s from a point 1 0 m above the ground At what distance above the ground do the ball and the toy cross paths

A 17th century scientist Galileo observed that for frictionless surfaces X and Y a ball released from the top reaches the top on the other side If Z is also a frictionless horizontal surface how far would a ball roll when released from the top of the inclined surface 1 h X 2 2h h h Z 3 It will never stop 4 3h

Two particles A and B move in x y plane such that they have constant acceleration a 10 m s and a 5jm s respectively The velocities of particles at t 0 are 57 20 m s and Ug 2 5i 10 m s At time t 0 particle A is at origin and particle B is at point having coordinates 5 m 0 Find the instant of time in seconds at which angle between velocity of A and velocity of B is 180

After starting from rest a body travels a distance of 3S with uniform acceleration then moves with uniform velocity for a distance of 2S and finally comes to rest after moving further 5S under uniform retardation What is the ratio of average velocity to maximum velocity O O 74 5 9 3 7 9

A boat covers a given distance in 6 h moving down stream of a river It covers the same distance in 10 h moving upstream The time in hour it takes to cover the same distance in still water is O O O 6h 7 5 h 10 h 15 h

7 The velocity of a river current is u A man crosses the river with velocity v making an angle with the direc tion of the current If the width of the river is d find the time taken to cross the river and the displacement of the man in the direction of the current What would be the minimum time required for crossing the river In what time could he reach exactly the opposite point HIS OF

2 A plate of mass M is kept floating in a horizontal position by shooting particles of mass m vertically up from below Each particle hits the plate with a speed of u and rebounds with the same speed Calculate the number of particles that should be shot per unit time to keep the plate in equilibrium 1 3 Mg mu Mg 2mu 2 4 2Mg mu 4Mg

The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to half the magnitude of vector B What is the angle between A and B O O O O 30 45 150 120

4 A particle starts with a velocity of 2 ms and moves in a straight line with a retardation of 0 1 ms 2 The first time at which the particle is 15 m from the starting point is a 10 s b 20 s d 40 s c 30 s C

A boy throws the balls vertically up in air in such a way that when the first one is at the highest point he throws the second How high each ball will rise if he throws two balls per second O O O 4 9 m 2 45 m 9 8 m

At t 0 a bird at rest starts flying horizontally from the top of a tower of a height 1 25 m with initial acceleration of 1 5 m s At the same instant a stone is projected from point B on ground as shown If stone hits the bird during its downward motion at an angle 45 to the horizontal the time in seconds at which sto will hit the bird is take g 10 m s Ignore air resistance on stone BAB 1 25 m

1 The position of a particle is x y plane is described by the variables x at and y 2at Then the acceleration of the particle 1 is 6a at t 0 2 is 6a at t 1 3 is 3a at t 0 4 is 3a at t 1

Relation between average velocity Vay of a body and time t is shown in the graph If av during the time interval considered the body did not change direction of motion draw a graph between instantaneous velocity of the body and time 1 0 1 2 3 4 t s

The displacement of a particle as a function of time is shown in the figure The figure shows that Displacement 10 10 30 A The particle starts with certain velocity but the motion is retarded and finally the particle stops B The velocity of the particle is constant throughout C The acceleration of the particle is constant throughout D The particle starts with constant velocity then motion is accelerated and finally the particle moves with another constant velocity

13 A person is standing on a truck moving with a constant velocity of 14 7 m s on a horizontal road The man throws a ball in such a way that it returns to the truck after the truck has moved 58 8 m Find the speed and the angle of projection a as seen from the truck b as seen from the road

2 A body starts from rest with acceleration 2 m s for some time then retards with 4 m s and finally comes to rest If the total time of journey is 15 sec then what will be maximum velocity fax 3g vid ufe uch and free star 2 m s 4 m s 15 sec 1 15 m s 2 20 m s 3 30 m s 4 40 m s

A train of 150 m length is going towards east with speed 10 m s A bird flies at a speed of 5 m s towards west The time taken by the bird to cross the train is 150 m 10 m s farm a 5 m s fra 13 35 1 12 s 2 8 s 3 10 s 4 15 s

A particle is projected vertically upward with velocity w from the top of tower of height H Its velocity at a depth h below the point of projection is thrice of its velocity at a height h above the point of projection The time at which it hit the ground is V 1 2 Hg g 2 3 4 9 9 V 1 2H g 1 2gH v 1 1 29H

Suppose two particles 1 and 2 are projected in vertical plane simultaneously 1 2 hy hefuz da ugfa f e 160 m s K X Their angles of projection are 30 and 0 respectively with the horizontal Let they collide after a time t in air Then 3 y 300 fast C 2 A 0 sin and they will have same speed just before the collision 0 sin 1 acha ugd 3 ud Aga zm B 0 sin and they will have different speed just before the collision 1 sin 1 am Tuche Ah ugd zam alm 100 m s z ay a Thadi as Correct Answer 30 I x 1280 3 960 m Correct Answer ef D It is possible that the particles collide when both of them are at their highest point ug fya f atat gu ad chud g da gu 7 1 A T

Finding the Average Speed Read and study the given scenario Then answer the questions that follow Mang Kevin is a vendor who lives 7km upstream from the town When the current is 4 km hr he can paddle his boat downstream to reach the town and come back in 2 hours 1 Make a mathematical model 2 representing the scenario What is the average paddling speed in still water

3 A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward followed again by 5 steps forward and 3 steps backward and so on Each step is 1 m long and required 1 s to cover How long the drunkard takes to fall in a pit 13 m away from the start 2 21 s 1 9 s 2 22

For a positively charged particle moving in a x y plane initially along the x axis there is a sudden change in its path due to the presence of electric and or magnetic fields beyond P The curved path shown is in the x y plane and is found to be non circular P Which one of the following combination is possible 1 E ai Buck

For the velocity time graph below the distance covered by the body in last two seconds of its motion is what fraction of the total distance covered by it in all the seven seconds Velocity m sec 1 10 2 1 2 2 3 4 5 Time sec 4 3 3 6 7 4 2 3

During inelastic collision between two bodies whi of the following quantities always remain conserve 1 Total kinetic energy 2 Total mechanical energy 3 Total linear momentum 4 Speed of each body

A ring of radius 10 cm is initially at the coordinate plane such that it touches the positive sides of the x and y axes at P and Q respectively The ring starts rolling at a speed of 1 rev min along the positive x axis The coordinates of the point Q after 2 minutes and 45 seconds are a 50 20 c 55T 10 0 b 55 10 d 50 10 0

A a ball is thrown with a speed of v 15 0 m s at a target that is at height h 6 m above the level the ball is released If one wants the ball s velocity to be horizontal at an instant it reaches the target a at what angle above the horizontal must the ball be released b what is the horizontal distance from the release point to the target c what is the speed of the ball just as it reaches the target

A train starts from rest at S 0 and is subjected to acceleration as shown a m s 6 30 S m Change in velocity at the end of 30 m displacement is 20 m s Velocity of the train for S 10 m is 10 m s The maximum velocity attained by train is 14 m s The maximum velocity of the train in between 15 m and 16 ml

A boy is going from his home to a stationary shop He moves 100 m north then takes left and moves 50 m in the west direction and reaches the shop If he takes 5 minutes to reach the shop the velocity of the boy in m s is A 2 i 1 B 1 1 c 1 D 1 1

1 Two balls are projected from the same point horizontally in the same direction with velocities 7m s and 4m s respectively They hit the ground 12 meters apart Find the height of the point they were thrown from Assume g 10m s