Kinematics Questions and Answers

17 A particle starts moving rectilinearly at time t 0 such that its velocity v changes with time t according to the equation v t2 t where t is in seconds and v is in m s The time interval for which the particle retards is a t 1 2 b 1 2 t 1 c t 1 d t 1 2 and t 1 18 The velocity n and displa

A body accelerate from rest with an accele ration of 1m s 2 for 10seconds Then the body starts moving with constant velocity for 20seconds There after the body retard s to come to rest if the retardation is 1 2 m s 2 then find the total distance moved by body

wo identical blocks each of mass 200 g and charge 0 8 C are at rest on a horizontal surface having a separation of 20 cm between them If g is 10 m s and 1 48 9 x 10

From top of a tower 100 m high a ball is dropped and at th same time another ball is projected vertical up from groun with speed of 40 m s The two balls will meet g 9 8 m s 56 m above ground 30 6 m below the top hr mi 40 8 m below the top

For the car of a particular make the braking distance was found to be 10 m 20 m 34 m and 50 m corresponding to velocities of 11 15 20 and 25 ms which are nearly consistent with the above formula distance is an important factor considered in setting speed limits for

The angle of projection of a body is 15 The other angle for which the range is the same as the first one is equal to 30 45 60 75

The position x time t graph of one dimensional motion of a body of mass 0 5 kg is shown The magnitude of each impulse is x m 2 1 N s 2NS 6 8 10 12 t s

13 A projectile is projected at an angle 60 with horizontal with speed 10 ms The minimum radius of curvature of trajectory is a 2 55 m c 10 m b 2 m d None of these

29 Raindrops are falling vertically with a velocity of 10 m s To a cyclist moving on a straight road the raindrops appear to be coming with a velocity of 20 m s The velocity of cyclist is

12 A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 ms at an angle of 30 with the horizontal How far from the throwing point will the ball be at the height of 10 m from the ground take g 10 ms sin 30 12 cos 30 3 2 a 5 20 m c 2 60 m b 4 33 m d 8 66 m

KN0102 2 The graph between the displacement x and time t for a particle moving in a straigh line is shown in figure During the interval OA AB BC and CD the acceleration of the particle is 1 2 3 4 OA displacement A B time AB 0 0 0 0 C BC CD 0

56 A block of mass m is placed on a wedge of mass M There is no friction between the block and the wedge The minimum coefficient of friction between the wedge and the ground so that wedge does not move is m cos 0 m sin e a b 0 2 M m cos 0 m cos e sine mcos A d 0 2 M m cos m cose sine m 0 M msin e 0

A projectile is thrown at an angle with an inclined plane of inclination as shown in figure Find the relation between 3 and 0 if a Projectile strikes the inclined plane perpendicularly to the inclined plane Projectile strikes the inclined plane horizontally to the ground b

44 A ball B is at 300 cm distance from origin on a line 37 above horizontal Another ball A is projected directly aiming B with initial velocity 700 cm s At the same instant B is released from A b 80 cm AB 300 cm B 37 its position How far will B have fallen when it is hit by A a 90 cm c 70 cm d 60 cm

49 The figure shows a block of mass M attached to an uncompressed spring of spring constant k resting on a frictionless surface A bullet of mass m travelling with a constant horizontal velocity v hits the block and get embedded inside What is the maximum compression of the spring A v m B v C M m M UV k m mv M WWW

A particle is dropped from an elevation of H 100 m After the particle is released another particle is projected vertically up from the ground with a speed v 10 m s after time t 1s Determine the time when the two particles meet 10 m s Take acceleration due to gravity g A 5 75 s B 4 75 s C 6 75 s

0 of same brake force recocr IN If a body is projected upwards or falls freely then the direction of acceleration is downwards in both cases downwards T In the absence of air resistance the velocity of projection is equal to the velocity with which the body strikes the ground 00 In case of air resistance the time of ascent is less than time of descent for a body projected vertically upward t 64 For a body projected vertically upwards the magnitude of velocity at any given point on the path is same whether the body is moving in upwards or downward direction

41 A ball is projected so as to pass a wall at a distance a from the point of projection at an angle of 45 and falls at a distance b on the other side of the wall If h is height of wall then a h a 2 c h 2 ab a b b h b 2 ab a a b d h

62 After a ball rolls off the edge t 0 its velocity as a function of time is given by V 1 21 9 8t able at time where is in meters per second and t is in seconds The ball s displacement away from the edge of the table during the time interval of 0 380 s for which the ball is in flight is given by Ar 0 380 s dt 0 To perform the integral you can use the calculus theorem A Bf x dx A dx B f x dx You can think of the units and unit vectors as con stants represented by A and B Perform the integra tion to calculate the displacement of the ball from the

If a 41 3j and b are two vectors perpendicular to each other in the xy plane Find all vectors in the same plane having projection 1 and 2 along a and b respectively Find the valuafak

Find the average speed on the particle in 3 seconds if x coordinate of the particle varies as x 2t t 3 A 1 B 3 C 5 Tich x 2t 1 u Rafa stai at

12 Assertion When a body is dropped or thrown horizontally from the same height It would reach the ground at the same time Reason Horizontal velocity has no effect on the vertical direction

A brick is given an initial speed of 5 ft s up an inclined plane at an angle of 30 from the horizontal The coefficient of sliding or static friction is 3 12 After 0 5 s how far is the brick from its original position You may take g 32 ft s

V A particle moving along a straight line has velocity v m s when it covers a distance x along positive x axis The relation between two quantities is v 49 x When the velocity of particle is 1 m s its acceleration will be 1 m s 7 m s 2 m s C L

From top of a tower 100 m high a ball is dropped and at the same time another ball is projected vertical up from ground with speed of 40 m s The two balls will meet g 9 8 m s 56 m above ground 30 6 m below the top 40 8 m below the top

Two ends of a train moving at constant acceleration pass a point with speed of 12 m s and 24 m s respectively The speed with which middle point of the train passes the same point is approximately 16 m s O 19 m s 22 m s 20 m n

A particle moves clockwise in a circle of radius 1m with centre at x y 1m 0 It starts at rest at the orig it m s i How long does it take to travel halfwa at time t 0 Its speed increases at the constant rate of around the circle ii What is the speed at that time

A ball is thrown vertically upwards with velocity of 20 m s from top of a tower 25 m high What is maximum height reached by ball from ground g 10 m s 30 m 40 m 45 m 75 m

4 A space ship moving away from the earth with velocity 0 6c fires a rocket whose velocity relative to the spaceship is 0 7c away from the earth What will be the velocity of the rocket as observed from the earth 1 Point 1 3c

The position of the bumper of a moving car is given by x t a bt ct6 where a 2 17 m b 4 80 m s2 and c 0 100 m s6 a Find the average velocity of the car in the interval 13 00 s and t2 9 00 s b Find the velocity of the car at t 2 00 s and t 5 00 s

b A sports car speeds past a stationary police motorbike at 85 km h The instant the speeding car passes the police motorbike the police begin their pursuit If the speeding car maintains a constant velocity and the police motorbike accelerates with a constant acceleration of 4 2 ms2 how long in time does it take the police motorbike to catch up to the speeding car 3 marks

A jet plane lands with initial speed of 100 m s and comes to rest after 20 s what was its acceleration in m s Select one a 80 b 80 C 5 d 5

A force represented as show in figure acts on a body having a mass of 16 kg The velocity of the body at t 10 s if the body starts from rest F N 75 50 1 100 m s 3 49 m s 5 10 t s 2 50 m s 4 39 m s

Plz explain clearly A stone is projected from the point on the ground in such a direction so on to hit a bird on the top telegraph post of height h and then attain maximum height 2h above the ground If at the instant of projec bird were to fly away horizontally with uniform speed v 2 2 1 m s Find the horizontal velocity of the s if the stone still hits the bird while descending A car goes on horizontal aire

Q 1 A motorboat going downstream overcame a raft at a point A T 60 min later it turned back and after some time passed the raft at a distance 1 6 0 km from the point A Find the flow velocity assuming the duty of the engine to be constant

he position versus time for a certain particle moving along the x axis is shown in the figure below Find the average velocity in the following time intervals x m 10 8 6 4 A 2 1 2 3 4 5 6 7 8 2 a 0 to 2 s b 0 to 4 s c 2 to 6 s d 2 to 7 s e 0 to 7 s m s m s m s m s

9 A ship A is moving Westwards with a speed of 10 km h and a ship B 100 km South of A is moving Northwards with a speed of 10 km h The time after which the distance between them becomes shortest is 2015 a 5 h b 5 2h c 10 2h d 0 h The position vector of a particle R as a function of

1 In going from one city to another a car travels 75 km north 60 km north west and 20 km east The magni tude of displacement between the two cities is Take 1 2 0 7 a 170 km c 119 km b 137 km d 140 km

5 The force acting on an object varies with the distance travelled by the object as shown in figure Work done by the force in moving the object from x 0 m to x 4m is AF N 1 4 J 3 4 J 4N 6 2 x m 16 3 J 4 12 J

27 Acceleration of a particle moving in x y plane varies with time tas a t 3t j Here a is in m s2 and t in second At time t 0 particle is at rest at origin Mass of the particle is 1 kg Find the net work done on the particle in first 2 s a 40 J c 16 J b 34 J d 48 J

Fig shows the displacement time graph of a particle moving on the X axis XA 5 t A the particle is continuously going in positive x direction B the particle is at rest C the velocity increases up to a time t and then becomes constant D the particle moves at a constant velocity up to a time t and then stops

13 A baseball is popped straight up into the air and has a hang time of 6 25 s Determine the height to which the ball rises before it reaches its peak Hint the time to rise to the peak is one half the total hang time

7 A rocket is fired vertically from the ground It moves upwards with a constant acceleration of 10 m s After 30 seconds the fuel is finished After what time from the instant of firing the rocket will it attain the maximum height g 10 m s 1 30 s 2 45 s 3 60s 4 75 s

Two particles are projected simultaneously in the same vertical plane from the same point both with different speeds and at different angles with horizontal The path followed by one as seen by the other is a a vertical line b a parabola c a hyperbola d a straight line making a constant angle 90 with horizontal

Two balls are dropped from different heights at different instants Second ball is dropped 2 seconds after the first ball If both balls reach the ground simultaneously after 5 seconds of dropping the first ball then the difference between the initial heights of the two balls will be g 9 8m s 1 58 8 m 2 78 4 m 3 980 m 4 1176 m

178 A player throws a ball that reaches to the anothe player in 4s If the height of each player is 15 the maximum height attained by the ball from t 5 ground level is 1 19 6 m 3 23 6 m 2 21 1 m 4 25 1 m

Drops of water fall from the roof of a building 18m high at regular intervals of time When the first drop reaches the ground at the same instant fourth drop begins to fall What are the distances of the second and third drops from the roof 1 6 m and 2 m 2 6 m and 3 m 4 4 m and 2 m 121 m and 2 m

8 An engineer is designing the runway for an airport Of the planes that will use the airport the lowest acceleration rate is likely to be 3 m s The takeoff speed for this plane will be 65 m s Assuming this minimum acceleration what is the minimum allowed length for the runway

1 Indian space research organization ISRO designed a run way to test air crafts Being famous for JUGAAD Indians designed a run way where they can efficiently test the engines of a rocket as well as jet During test run rocket motor was fired from rest it accelerated constantly until its fue was exhausted after which it ran with hr constant speed The fuel was exhausted at mid point of the run way When jet motor was tested at the same site it started from rest and covered the entire run way with constant acceleration taking exactly the same time as rocket Calculate the ratio of their acceleration

A block of mass M 1kg lies on a smooth horizontal floor A bullet of mass 0 1kg is fired horizontally with a velocity u 110m s and gets embedded in the block The combined mass is set into motion and encounters a rough inclined plane of inclination 37 and length 1 8m in its path It starts moving up the inclined plane 0 5 reaches the topmost point and finally lands on the horizontal floor Assuming that the mass is not jerked when it starts up on the inclined plane the horizontal distance covered by the combined mass while it is not in contact with the horizontal floor is approximately in m