Kinematics Questions and Answers

1 A cart moving with horizontal velocity magnitude v ejects a ball with a velocity magnitude v in the vertical direction relative to the moving cart The ball must pass horizontally through a small stationary hoop fixed at some height h as shown in figure and lands on the second hoop that is fixed horizontally on the cart and centered at the launch point Let g be gravitational acceleration Then which of the following is are CORRECT You may ignore air resistance and any rolling friction on the cart A h 155 D V d h 2g 2v1V2 B d g C Ball moves in vertical direction with respect to cart 1 1 CAL

9 An arrow leaves the bow with the following initial conditions speed V 75 m sec angle of 43 height of 2 5 m Suddenly the arrow encounters a gust of wind with V 12m sec blowing at an angle of 82 as shown What is the flight time of the arrow How far has it traveled 82 43 x

A car speeding at a constant 48 0 m s passes a county sheriff sitting at rest along side of the road The sheriff immediately as the car passes starts accelerating at a constant rate The sheriff catches is directly behind the speeder in 82 0 s What was the sheriff s constant acceleration in m s2

A vehicle is traveling at 7 95 m s down a hill when the brakes are hit The hill makes an angle of 4 10 The coefficient of kinetic friction between the tires and the road while braking is 0 580 What is the magnitude of the acceleration Answer should be in m s

Small plane pilots regularly compete in message drop competitions dropping heavy weights for which air resistance can be ignored from their low flying planes and scoring points for having the weights land close to a target A plane 70 m above the ground is flying directly toward a target at 48 m s Part A At what distance from the target should the pilot drop the weight Express your answer with the appropriate units

A certain airplane has a speed of 265 5 km h and is diving at an angle of 0 30 0 below the horizontal when the pilot releases a radar decoy see the figure The horizontal distance between the release point and the point where the decoy strikes the ground is d 609 m a How long is the decoy in the air b How high was the release point a Number Units 10

A particle travels th of its journey with speed 20 m s then find speed during remaining journey so tha average speed during complete journey is 32 m sec 1 40 m sec 2 42 m sec 3 48 m sec 4 50 m sec

42 A person is an elevator accelerating upwards with an acceleration of 2 ms 2 tosses a coin vertically upwards with a speed of 20 ms After how much time will the coin fall back into his hand g 10 ms 2 10 1 sec 3 2 4 sec 5 3 sec 4 3 20 sec

Read each statement below carefully and state with reasons and examples if it i true or false A particle in one dimensional motion a with zero speed at an instant may have non zero acceleration at that instam b with zero speed may have non zero velocity c with constant speed must have zero acceleration d with positive value of acceleration must be speeding up

A swimmer wishes to cross a river of width 500 m River flows at a speed of 4 m s Swimmer can swim in still water with 3 m s Then Minimum time in which he can cross the river is 166 67 s Drift cannot be zero when he crosses the river in least time Drift can be zero if swimmer chooses an optimum direction The minimum time in which he can cross the river is 125 s

A body starting from rest accelerates uniformly and attains a velocity of 15 m s in 15s Find in acceleration and the distance it covers in that time 1 m s 112 5 m A body moving with a velocity of 10 m s accelerates uniformly and covers 300 m when in velocity becomes 20 m s Find the time taken to achieve this velocity 20 s

2 26 At the moment t 0 a stationary particle of mass m experiences a time dependent force F kt t t where k is a constant vector t is the time during which the given force acts Find a The momentum of the particle when the action of the force discontinued b The distance covered by particle while the force acted Ans 3 6 dt k14

Find velocity and acceleration for the system described in the problem using a rotating coordinate system A particle moves in a plane elliptical orbit described by the position vector r 2b sin wt i bcos wtj a Find v a and the particle speed b What is the angle between v and a at time 77 200

3 Two cars move in the same direction along parallel roads One of them is a 100 m long travelling with a velocity of 7 5 ms How long will it take for the first car to overtake the second car a 24 s c 60 s c 40 s d 80 s

In the arrangement as shown block A of mass 3 kg moves towards left with velocity 10 m s Initially block A is 100 m from pulley on a smooth surface Block B is of mess 2 kg g 10m s A A At t 1 sec velocity of A will be 6 m s towards left B A will stop at t 4 5 sec C Block A will be at a distance 108 m from pulley at t 5s D Block A will again be a distance of 100 m from ullow at t 10s K 100 m BY

4 sina ucosa 5 A ball of mass m is thrown from ground with speed u at an angle 0 with horizontal Find the power when the ball is at maximum height of the trajectory 1 mgu cose 2 mgucose 4 Zero 4 20 A ur Its 2

5 A balloon is rising with uniform speed 6 ms 1 At a height 3 2 m from the ground a stone is dropped from the balloon The time taken by the stone to strike the ground is g 10 m s 3 2 m 1 0 4 s 2 0 8 s 3 0 6 s 4 1 6 s h ut jgth 7 3 2 6t 54 57

A body is projected with a velocity of 20 m s making an angle 60 with horizontal The radius of curvature in metre at a point where the velocity vector makes an angle 30 with horizontal is nearly g 10 m s

An aeroplane is to go along straight line from A to B and back again The relative speed of aeroplane with respect to wind is V The wind blows perpendicular to line AB with speed v The distance between A and B is 1 The total time for the round trip is 21 A v C 2V 1 1 1 2 B 217 p 21 D 1 X

A man in a balloon rising vertically with an acceleration of 4 9 m s2 releases a ball 2 s after the balloon is let go from the ground The greatest height above the ground reached by the ball is g 9 8 m s a 14 7 m c 9 8 m b 19 6 m d 24 5 m 10

A stone is projected on an incline plane which is inclined at an angle a with horizontal It has found that the stone strikes the inclined plane perpendicularly Initial velocity of projection is at an angle B with inclined plane Select the CORRECT alternatives A If velocity of projection is double then angle at which stone strikes the incline plane remains same proies ion decreases with time for above condition quer

A person throws balls into air after every second The next ball is thrown when the velocity of the first ball is zero How high do the ball rise above his hand a 2 m b 5 m c 8 m d 10 m

Question 26 The displacement in metres of a body varies with time t in second as y t2 t 2 The displacement is zero for a positive of t equal to a Is b 2 s c 3 s d 4 s

Two small solid sphere each of mass m 1 kg are thrown at the same time with initial velocity V 200 3 m s and angle 30 with the horizontal Sphere 2 is thrown at a height h 1 m above sphere 1 as shown in the figure Counting the gravitational force between the two spheres calculate the change of distance Sh 108m between the two spheres at the moment sphere 1 hits the ground Ground You may take the distance between the two spheres as constant h in your derivation for the gravitational force because dh h G 20 10 Nm kg and 10 m s 3 Your Answer Inattempted Rate this question

65 Horizontal electric field exist as shown in figure A 68 Th a mass m with charge q attached to a massless rod of length is released from the position shown in figure find the angular velocity of the rod when it di 1 3 69 Fo ke CO passes through the bottom most position 1 3g 45 q m 2 2g 15g E mg q

4 10 2 m s 3 10 A ship A is travelling due east at 10 m s instant another ship B is 1 km due east of A and travelling due north at 10 m s The minimum dis tance between the two ships during subsequent motion is 21 X 1000 1 1000 m 707 m 500 m 2 3 4 zero that 10 10 0001 10000 0 707

1 18 Water drops are falling down at regular time intervals from ceiling such that when 1st drop is about to hit the ground the nth drop is starting from the ceiling as shown If H is vertical distance between the ceiling and the ground then the distance of rth drop from the ceiling is given by Ceiling n r H n 1 n H pth 2nd 1st Surface 2 4 n r H n 1 r H n vertically upward considering cons shown by 3 23 A car s retards such t cover

A particle coveres one third of the total distance between two points with a constatn speed of 3 0 m s and the remaining two third distance in two spells of equalt duration with constant speeds of 4 0 m s and 5 0 m srespectively What is the average speed of the particle for the entire motion between the two points A 2 4 m s B 3 8 m s C 4 0 m s D 6 0 m s

A stone is thrown downward at an angle of 55 0 degrees below the horizontal from a bridge 60 0 m above a river If its initial speed is 40 0 m s where and with what speed will it strike the water

j m s The arts to run in which he e first ball a height 1 40 A particle moves for total time T sec in a straight line in three consecutive parts such that its acceleration during the first second and third parts is in the ratio 1 2 7 The distances covered in the first and the third parts are a and b meters while the time taken for each of the ist seconds Find the average velocity of the particle during the second part Ans b 3 2t a b 41

33 A body is thrown at some angle from the ground Sec The magnitude of change in velocity of body in 5 s if it is still in air is g 10 m s 7 6 ce 1 50 m s 2 25 m s 10 5 si 3 Zero 4 Data is insufficient 34 The equation of trajectory of a projectile is given as 2021 QUAL CAMEEN BAWLESIASULAL X 2021 08 11 14

A car accelerates from rest at a constant rate o for some time after which it decelerates at a constant rate B to come to rest If the total time elapsed is t evaluate a the maximum velocity attained and b the total distance travelled a Let the car accelerates for time t and decelerates for time t then t t 1 and corresponding velocity time graph will be as shown in fig 1 31 0 t From the graph a slope of line AB and slope of line OB 11 max a B t v max t a V 1 b Total distance area under v t graph max t v B max 1 2 a a t a B xtxv max 1 2 t xtx a t a B 1 a t 2 B

1 A plane which can travel at a speed of 300 kmh in still air heads due north The plane is blown off course by a wind so that it travels on a bearing of 010 at a speed of 280 kmh i Find the speed of the wind 3

Question No 2 A particle starts to move in positive x direction from origin and its velocity varies with x as v 4 x m s If average velocity of particle in m s averaged over th the particle has cover 400 m distance is v then find the value of 10

A car on the cross road is moving towards east at a speed of 40 km hr Another car which is 1 km south of the crossing is approaching the crossing with the same speed Their closest distance of approach will be

a balloon rising vertically upwards with constant acceleration 1 5 m per sec sq uare After 8 sec a stone is dropped fro m it find out 1 displacement of stone when it reach es ground 2 time taken by stone to reach on grou nd 3 total distance travelled by stone afte r releasing it

5 Acceleration time a t graph of a particle moving on the x axis is shown in the figure If at the instan t 0 the particle was moving with a velocity of 2 m s in the positive x direction what is its displacement in the time time interval from t 0 to t 12 s A 132 m a m s B 144 m 4 0 0 6 C 156 m 12 t s HEOSTAD D None of these

A body at rest is imparted motion to move in a straight line It is then obstructed by an opposite force then 1 the body may necessarily change direction 2 the body is sure to slow down 3 the body will necessarily continue to move in the same direction at the same speed 4 none of the above

A car is moving in x direction for 29 seconds with a velocity of 10m s then the car increases its speed and travels another 24 4 seconds with a velocity of 20 m s What is the average velocity of the car during total travel in m s Assume velocity increase instantaneous Do not type units in to the box only numerical answer required

6 Susie can swim at 4 mi hr and run at 20 mil hr She is in a race from the southern tip of a small island located 1 mile from the nearest point A on a straight shoreline The race ends at point C which is 4 miles from point A To what point B should Susie swim in order to reach point C in the least amount of time Your answer will be the distance x in miles between points A and B No need to justify your answer here island

d remains unchanged 28 A particle starting from rest falls from a certain height Assuming that the acceleration due to gravity remain the same throughout the motion its displacements in three successive half second intervals are S S and S then a S S S 1 5 9 b S S S 1 3 5 c S S S 9 2 3 d S S S 1 1 1

Two trains A and B of lengths 300 m and 100 m respectively are running on parallel tracks with velocities 108 km m and 72 km h respectively a If both the trains are travelling in the same directions then how long will A take to overtake B b If both the trains are travelling in the opposite directions then how long will they take to cross each other

Two particles A and B move with constant velocities v and v At the initial moment their position vectors are r1 and r2 respectively The condition for particles A and B for their collision is 1 71 72 T1 7 2 7 V 72 V2 22 21 22 27 3 r U T2 V 4 1 1 V V

Two trains move in opposite direction along parallel tracks Both of them are 100 m long and each travelling with a velocity of 12 5 m s How long will it take for the first train to cross the second train 085 O4s 065 20 s

A projectile is thrown at a certain angle with some speed towards a perfectly elastic wall from a distance of 4 m The range of the projectile in the absence of the wall would have been 10 m Find the new range of the projectile in the presence of the wall

successive seconds by a body accelerated uniformly from rest Time intervall Distance O 4ms 1 What is the speed of the body at the end of 4th second x is in meter 08ms 1 V 261016 14 ms 1

Choose the incorrect statements 1 In projectile motion from ground to ground projection the speed of the projectile first decreases then increases to the same value 2 Horizontal component of velocity is constant in a projectile motion under gravity 3 In a projectile motion the velocity at its heighest point is zero 4 For two stones projected simultaneously from same point with same speed at different angles with horizontal their trajectories may intersect at same point

1 5 km h 2 5 2 3 10 km h 4 4 km h 14 The angle of projection of a projectile which is TC 8 projected with certain velocity from ground is horizontal and its horizontal range is R The angle with the horizontal for another projectile having same range R and speed is NCERT Pg 78 2 3 4 3n 8 H4 13 TL 6 with SECTION B Objective Type Questions The position coordinates of a projectile thrown from ground are given by y 3t 5t2 m and x 4t m here t is in second x is horizontal and y is vertical horizontal range of the projectile is 5 6 7 8

A projectile is fired with velocity vo from horizontal surface making an angle with vertical If the wind imparts constant horizontal acceleration a to the left then at what angle projectile must be fired so that is returns to the point of projection Assume g to be uniform VE a

sec Q 17 A ball is thrown vertically upwards from the ground It crosses a point at the height of 25 m twice at an interval of 4 secs The ball was thrown with the velocity of A 20m sec B 25 m sec C 30m sec D 35 m sec Q 18 A particle is projected vertically upwards from a point A on the ground It takes t time to reach a point B but it still continues to move up If it takes further t time to reach the ground from point B