Kinematics Questions and Answers

Adjacent graph is drawn for particle along straight line motion a Acceleration v velocity Find displacement of particle in meters from re till it acquires velocity 2 ms 1 3 4 v m s2

A In the case of ground to ground projection of a projectile from ground the angle of projection with horizontal is 0 30 There is no point on its path such that instantaneous velocity is normal to the initial velocity R Maximum deviation of the projectile is 20 60

a 15 m b 25 m c 35 m Q 95 A stone is dropped from a height h Simultaneously another stone is thrown up from the ground which reaches a height 4 h The two stones cross each other after time a h 8g b 8hg c 2gh d h 2g

5 A block is kept on a fixed inclined plane of inclination 60 as shown Coeficient of friction 1 between the block and the incline is To keep the block at rest minimum external force should be applied along the vector 1 31 1 3 3 1 1 60 X 2 i 3 4 31 1

A At the highest point the velocity of projectile is zero R At maximum height projectile comes to rest

10 A particle starts from rest at x 0 and acceleration varies with x as shown in the figure Then a m s 4 x m 1 The particle comes to rest at x 20 m 2 Maximum velocity in positive x direction is 4 5 m s 3 Velocity at x 10 m is 60 m s 4 Distance covered by particle till it returns to initial position is 80 m

tan a Velocity v versus time 1 graph of a particle moving in a straight line is shown in the figure If tan B particle till the time its velocity becomes zero is v m s 1 s 2 then average speed of the E 36

Three balls A B and C are projected from ground with same speed at same angle with the horizontal The balls A B and C collide with the wall during a flight in air and all three collide perpendicularly and elastically with the wall as shown in figure If the time taken by the ball A to fall back on ground is 4 seconds and that by ball B is 2 seconds Then the time taken by the ball C to reach the ground after projection will be

24 A ball rolls off the top of a stair way with a horizontal velocity 10 10 m s If the steps are 0 25 m high and 5 m wide then the ball will hit the edge of the nth step where nis 1 6 2 2 3 4 4 3

A cylinder is placed on a horizontal surface particle is projected with speed u and it crosses the cylinder by just touching at two points as shown in figure Then the initial speed with which the mass projected is vs The value of x is

A box of mass 4 kg placed on a horizontal floor is acted upon by a horizontal force F that varies with time t as shown in the given graph If coefficient of static and kinetic frictions are 0 25 then which of the following conclusions can you arrive FIN

The acceleration of a particle moving along straight line decreases linearly from a value of 15 m s2 at t 0 It has zero value at t 5 s At what time the particle acquires its initial speed 1 8 s 2 10 s 4 17 s 3 15 s

A cylinder horizontal is placed on a surface A particle is projected with speed u and it crosses the cylinder by just touching at two points as shown in figure Then the initial speed with which the mass projected is 5x m s The value of x is EO

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 30 m s 40 m s O 15 m s O 20 m s

2 If linear mass density of a rod of length 3 m lying from y 0 to y 3 m varies as 2 y kg m then position of the centre of mass of the rod from y 0 is nearly at 2 1 7 m 4 2 7 m 1 2 m 3 2 5 m

Velocity v versus time t graph of a particle moving in a straight line is show tan a tan velocity becomes zero is v m s in the figure If 4 O 2 m s O 3 m s O 4 m s O 1 m s 2 then average speed of the particle till the time its s

A particle moves in the east direction with 15 m sec for 2 sec then northwards with 5 m s for 8 sec Average speed of the particle is A 1 m s 5 m s 7 m s 10 m s

he speed of a projectile at its maximum height 1 is 2 times of its inital speed u of projection Its range on the horizontal plane is u 2g 1 3 3u 2g 3u 2 20 2 4 3u g

46 Position time graph for a particle is shown in figure Starting from t 0 at what time t the average velocity is zero x m 10 9 8 6 5 3 2 1 1 1 s 2 3 s 3 6 s 4 7 s 1 2 3 4 5 6 7 8 9 10 11 12 13 s 1 t s X2Y V 2 B 1

3 Ground is g Both 2 3 The velocity v time 1 graph for a particle moving along x axis is shown in the figure The corresponding position x time f is best represented by 4 u h h h 4 1 3 2

95 Three hodies A B and C are projected with the same initial speed with angles of projections 30 45 and 60 respectively The body bodies having maximum range C Sards you 30 30 45 0 0 60 5o 3473 is Jodowass nog gee sons 2 A 3 A and B A B 500 ro sa 1 B A 5300530 B 4 3400 4 C

Two blocks of mass 10 kg and 2 kg respectively are connected by an ideal string passing over a fixed smooth pulley as shown in figure A monkey of 8 kg started climbing the string with constant acceleration 2ms 2 with respect to string at t 0 Initially the monkey is 2 4 m from the pulley Find the time taken by the monkey to reach the pulley 1 2 4 m 1 sec monkey 8 kg 2 kg Question Type Single Correct Type 10kg

49 Figure shows the position of a particle moving on the x axis as a function of time m 20 10 0 2 4 6t s 1 The particle has come to rest 4 times 2 The velocity at t 8 s is negative 3 The velocity remains positive for t 2 s to t 6 s 4 The particle moves with a constant velocity A particle moyen ninn

4 80 m 39 The position time graph for a body moving along a straight line between O and A is shown in figure During its motion between O and A how many times body comes to rest 1 Zero 2 1 time 3 2 times A

47 The velocity versus time graph of a body moving in a straight line is as shown in the figure below v m s C t s 1 The distance covered by the body in 0 to 2s is 8m 2 The acceleration of the body in 0 to 2s is 4 ms 2 3 The acceleration of the body in 2 to 3s is 4 ms 2 4 The distance moved by the body during 0 to 3 s is 6 m 5

A cubical block of side a is placed on the ground A particle is projected from ground with minimum velocity vo such that it crosses over the cube as shown Then B 181 Vo 3ga Vo 5ga 8 cos 1 3 3

Board Competitive Exams Motion in a Straight Line 131 29 Two objects A and B are moving with velocities and va respectively along positive x axis if v V then which of the following position time graphs is correctly showing the velocity of A and 87 3 2 1 M x m K

22 Two objects A and B are moving with velocities V and va respectively in the same direction The magnitude of relative velocity of Aw r t Bis 1 VA VB 3 VB VA 2 VA VB 4 VVB

A cyclist is 24 metres behind a bus If bus starts from rest with constant acceleration of 2m s while at same time cyclist moves with constant speed of 10m s then time when cyclist will overtake bus O O O 2 sec 4 sec 6 sec 10 sec

1 A ship A is moving Westwards with a speed of 10 kmh and a ship B 100 km South of A is moving Northwards with a speed of 10kmh The time after which the distance between them becomes shortest is A Oh C 5 2h A Incorrect Marked By You B Correct Not Marked By You B 5h D 10 2h

A boat which has a speed of 5 km hr in still wate crosses a river of width 1 km along the shortes possible part in 15 minutes The velocity of the river water in km hr is A 3 C 21 A Correct Skipped By You B B 4 D 1

A ball is thrown vertically upward with a velocity u from the top of a tower If it strikes the ground with velo 3u the time taken by the ball to reach the ground is g 3u 2 4 2u g 4u

A particle located at x 0 at time t 0 starts moving along the positive direction with a velocity v which varies as v a x then acceleration of particle is a is a constant 2 a x 2 a x 2 V constant

Question 11 Width of a river is 60m A swimmer wants to cross the river such that he reaches from A to B directly Point B is 45m ahead of line AC perpendicular to river Assume speed of river and speed of swimmer are equal Swimmer must try to swim at angle 8 with line AC Value of 0 is 1 37 C B A 2 53 River Flow 3 30 4 16

tan a Velocity v versus time t graph of a particle moving in a straight line is shown in the figure If tan B becomes zero is v m s 02 m s 3 m s 4 mis BA t s 2 then average speed of the particle till the time its velocity

Velocity of a particle moving along a straight changes parabolically with time according to the graph shown in figure Then its average velocity in the time internal t 0 to t 4 s 8 v m s 1 2 57 m s 3 6 15 m s 2 t s 4 2 4 m s 4 5 33 m s

Velocity of the ball A after collision with the ball shown in the figure is Assume perfectly inel and head on collision A 5 m s 2 m s O 2 kg B 5 kg

A particle is subjected to different types of accelerations in different initial condition position vector at t 0 V initial velocity a acceleration Column I Column II 1 F i j 11 F 21 III 1 IV 10 10 O II ii Q III ii P P Q iii V 101 R iv V 51 10 S In which of following case particle moves in straight line path O 1 i Q IV iv S i ii V 0 v 2 Column III a 21 3j a 5j a 10 a 21

Acceleration a of a particle moving in a straight line varies with its velocity v in m s as a 2 2 v m s Find the maximum possible speed of the particle assuming at f 0 particle was at rest

9 The amount of heat energy Q used to heat up a substance depends on its mass m its specific heat capacity s and the change in temperature AT of the substance Using dimensional method find the expression for s is Given that s L T K is 1 QmaT Qm 2 Q MAT m

SolveLancer Test A particle of mass m moves with a variable acceleration a which changes with distance covered x along a straight line as a k x where k is positive constant The velocity of the particle will be Consider the particle initially at rest SolveLancer Te a v b v c v d v 4k 3 x3 4k 11 3 3 x 2k 3 x3 2 x

questions Each question has 4 choices 1 2 3 and 4 out of which only one is correct A particle is thrown vertically up with velocity 10 m s from a point P which is 10 m above the ground Time after which particle reaches the ground g 10 m s 10 m s

The distance travelled by a particle is directly proportional to where this time elapsed Which of the following is correct regarding the motion of the particle Particle is moving with increasing acceleration Particle is moving with decreasing acceleration Particle is moving with decreasing retardation

Displacement of a truck moving along x axis is given by x at t 7 where tis time and a and 7 are positive constants Velocity of truck when its acceleration is zero will be O B 3y O a E Oa 28

The position vector of a particle R as a function of time is given by 7 R 4 sin 2nt 4 cos 2nt j where R is in metre t is in seconds and i and denote unit vectors along x and y directions respectively Which one of the following statements is wrong for the motion of particle a Acceleration is along R b Magnitude of acceleration vector is v R where v is the velocity of particle e Magnitude of the velocity of particle is 8 m s Both of the particle is a circle of radius 4 m

A bus is moving on a straight road toward North with a uniform speed of 50 km h If the speed remains unchanged after turning through 90 the increase in the velocity of bus in the turning process is a 70 7 km h along South West direction b zero c 50 km h along West Lako 7 km h along North West direction

The speed of a boat is 5 km h in still wate It crosses a river of width 1 0 km along the shortest possible path in 15 min The velocity of the river water is in km h 201 d 4 a 5 L c 3

Shown in the figure are the displacement time graph for two children going home from the school Which of the following statements about their relative motion is true after both of them started moving X C C T Their relative velocity A first increases and then decreases B first decreases and then increases C is zero D is non zero constant

44 Acceleration time graph for an obje motion is shown below a m s 4 8 2 4 10 2 t 10 s till t 18 s 3 t 18 s till t 20 s 18 20 20 m s In which time duration magnitude of change c velocity will be maximum 1 t 0 till t 10 s notion is required t s

45 Position time graph for four objects A D during their motion are shown in figures below In which case the object has constant negative acceleration throughout its motion A C 1 A 3 D t B D O L 2 C 4 B