Kinematics Questions and Answers

3 176 4 140 16 An object is projected from ground with speed 20 m s at angle 30 with horizontal Its centripetal acceleration one second after the projection is Take g 10 m s 1 10 m s 2 Zero 3 5 m s2 4 12 m s 17 A particle is moving on a circular path with constant 3 a cor q 21 A ball is thrown at an horizontal range is eq is possible only when 3 1 22 A ball is projected It will strike the gre Z 1 AST ET

A man at rest observes that rain is falling with the elocity of 20 m s at an angle 30 with the vertical The velocity with which the man should move on horizontal road such that rain again appears to fal at 30 with the vertical will be 1 20 m s 3 10 m s 2 20 3 m s 4 10 3 m s

A body is projected vertically upward with speed u The distance travelled by body in the last second of upwar journey is same as that of 1 Distance travelled in first second of downward journey 2 Distance travelled in last second of downward journey 3 Distance travelled in first second of upward journey A Roth 1 and 2

A cannon ball a has range R on a horizontal plane Ifh and h are the greatest heights in the twe paths for which this is possible then A R 4 hh 4h h B R C R 4 hh D R hh

The velocity of a body depends on time according to the equation v 20 0 112 The body is undergoing 1 Uniform retardation 2 Uniform acceleration 3 Non uniform acceleration 4 Zero acceleration

The vector subtraction of two vectors having same magnitude is equal to the magnitude of either vector The angle between two vectors is 2 60 1 0 3 120 4 90

up with velocity u reaches the maximum height h after T seconds Which of the following statements is true h 1 At a height from the ground its velocity is N E u 2 2 At a time T its velocity is u 3 At a time 2T its velocity is u directed downwards

A car of mass 200 kg is moving with a speed of 20 m s after 25 seconds the 10 m s then what is the change in momentum B 3000 kg m s A 4000 kg m s A force time graph for motion of a body is shown in figure The change F N A zero 2 B 4 Ns C 1000 kg m s 2 4 6 8 T s C 8 Ns D 2000 kg m s in momentum is D 16 Ns Laws of Motion 2020 21

30 If velocity v of a particle at a distance x from origin a x is given as v proportional to 1 3 1X 10 1 C then it s acceleration is 2 4

Two identical smooth balls are projected from points O and A on the horizontal ground with same speed of projection The angle of projection in each case is 30 see figure The distance between O and A is 100 m The balls collide in mid air and return to their respective points of projection If the coefficient of restitution is 0 7 find the speed of projection of either ball in m s correct to nearest integer Take g 10 ms 2 and 3 1 7 0 30 30 A

The displacement x of a particle moving alon x axis at time t is given by x2 2t2 6t Th velocity at any time t is

iii Consider n persons are standing at the vertices of a regular n sided polygon of side a Each person starts moving towards the person standing at the adjacent corner with same speed v The persons will meet at the centre of the polygon after time A a t V V COS 2 n A B D V C 2n n

In the given figure find the speed of pulley P a P b 2v cos 0 C 2v COSA d V 2 sin A

iv A point on the trajectory of a projectile projected at angle 0 with horizontal subtends angle a and P at the point of projection and point of landing then tane tana tan 4 v If R nH tan0 n 170

Il Based on Vertical Motion Under Gravity 4 A ball is thrown vertically upwards from the top of a tower with a velocity of 20 m s The ball strikes the earth after 5 s of its throwing What is the height of the tower What will be the velocity of the ball while striking the earth g 9 8 m s Ans 22 5 m 29 m s

A man running at speed of 5 km h finds the rain hitting his head vertically but he has to hold the umbrella at 30 with vertical while at rest The speed of rain is 1 5 3 km h 2 10 km h 3 5 km h

Two balls marked 1 and 2 of the same mass m and a third ball marked 3 of mass M are arranged over a smooth horizontal surface as shown in adjacent figure Ball 1 moves with a velocity v towards balls 2 and 3 All collisions are assumed to be elastic If M m the number of collisions between the balls will be m 1 One 1 2 m 3 M 2 Two

2 21 The initial velocity of a car is 5 m s It accelerates uniformly at 0 5 m s for 50 s and then retard uniformly at 2 m s Find the distance covered by the car before it comes to rest For how muc time is the car in motion 1100 m

Two particles A and B move with velocities v and v respectively along the x y axis The initial separation between them is d as shown in the fig Find the least distance between them during their motion d v A V C d v v d v B 2 d v D V B 00 A

Shown in the figure is a system of three particles having masses m 1 kg m 2 kg and m3 4 kg respectively connected by two springs The accelerations of A B and C at any instant are 1 m sec 2 m sec2 and 1 2 m sec2 respectively directed as shown in the figure The external force acting on the system is 1 1 N rightward 3 3 N righward 2 3 N leftward 4 zero a a a3 Avoooo Booooo m

17 A block of mass 200 kg is set into motion on a frictionless horizontal surface with the help of frictionless pulley and a rope system as shown in figure What horizontal force F should be applied to produce in the block an acceleration of 1 ms 2 a 1 ms 2 a 50 N b 100 N c 200 N d 10 N

Vector subtraction do Vector subtraction does not follow associative law i e A B If two vectors have equal magnitude i e A B a and 0 is the angle between them then 0 A B a a 2a cos 0 2a sin 2 ution 2 0 Special case If 0 60 then 2a sing a i e B A B a at 0 60 2 If difference of two unit vectors is another unit vector then the angle between them is 60 or If two unit vectors are at angle of 60 then their difference is also a unit vector In physics whenever we want to calculate change in a vector quantity we have to use vector subtraction For example change in velocity Av V V Illustrations strastion 31 The magnitude of pairs of displacement vectors are given Which pairs of displacement vectors cannot be add to give a resultant vector of magnitude 13 cm 1 4 cm 16 cm 2 20 cm 7 cm 3 1 cm 15 cm 4 6 cm 8 cm Resultant of two vectors A and B must satisfy A B R A B Ans 12

A ball of mass 50 g is dropped from a height of 20 m A boy on the ground hits the ball vertically upwards with a bat with an average force of 200 N so that it attains a vertical height of 45 m The time for which the ball remains in contact with the bat is Take g 10 m s 1 1 20th of a second 2 1 40th of a second 3 1 80th of a second 4 1 120th of a second

It took Gustavo 10 hours to drive to a football game On the way home he was able to increase his average speed by 18 mph and make the retur drive in only 7 hours Find his average speed on the return drive Step 2 of 3 Use the table from part 1 to help write a linear equation that represents the given word problem Use x to represent the unknown quantity Do not simplify your answer

28 A 6 kg bomb at rest explodes into three equal pieces P Q and R If P flies with speed 30 m s and Q with speed 40 m s making an angle 90 with the direction of P The angle between the direction of motion of P and R is about 2 127 4 150 1 143 3 120

8 A particle is projected at angle e with horizontal from ground The slop m of the trajectory of the particle varies with time t as 1 3 m m t 2 t 4 m A

A wooden bar of thickness d 20 cm is symmetrically placed on a hole made in a horizontal tabletop A bullet of mass m 20 g shot vertically up through the hole pierces the wooden bar Within the bar speed of the bullet reduces uniformly from u 100 m s at the bottom to v 80 m s at the top What should the minimum mass of the bar be so that it will not leave the tabletop Acceleration of free fall is g 10 m s 4

A body moving in a straight line has its motion described by x 2 3t 8t Find the equation its velocity and acceleration as functions of time

An elevator starts from rest with a constant upward acceleration It moves 2 m in the first 0 6 s A passenger in the elevator is holding a 3 kg package by a vertical string What is the tension in the string during acceleration Take g 9 8 m s

A car moving with a speed of 50 km hr can be stopped by applying brakes after at least same car is moving at a speed of 100 km hr the minimum stopping distance is 1 6m 4 24m 2 12m 3 18m

A stone is projected from horizontal ground with speed u and at an angle with horizontal Some how the acceleration due to gravity g becomes half that is g 2 immediately after the stone reaches the maximun height and remains same thereafter Assume direction of acceleration due to gravity always vertically downwards Answer the following questions The horizontal range of particle is

71 Position of a particle moving along x axis is given by x 2 8t 4t2 The distance travelled by the particle from t 0 to t 2 is 1 O 278 3 12 4 16

A body starts with initial velocity 30 m s and a retardation of 4 m s2 Find the distance travelled by the body in 8th second 8 30 8 16 1 Zero 3 2 m 240 30 240 30 Q10 2 1 m 4 112 m

1 Two persons P and Q start from points A and B respectively as shown in figure P and Q have speed v 12 m s in shown directions towards point O when the distance between P and Q is 120m then Q increases its speed to 15 m s Then find out who will reach the point O first A P B Q C both P and Q reaches simultaneously D Data is insufficient 240 m 180 m

A body is thrown in upward direction The velocity of body varies with position x as V4 1 3 2 X 4 O V 1

e of mass 2 kg The position time graph of a par moving along x axis is as shown in the figure The magnitude of impulse on the particle at f 2 sis NCERT Pg 110 x m 20

4 5 6 amp A ball is thrown at angle a 90 a 0 on inclined plane as shown in figure The minimum speed of the ball during the motion is u fign 1 u cos a 3 u cos a 0 a 2 u cos 0 4 zero

Illustration 6 Two inclined frictionless tracks one gradual and the other steep meet at A from where two stones are alowed to slide down from rest one on each track as shwon in Fig Which of the following statement is correct 1 Both the stones reach the botom at the same time but not with the sme speed 2 Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II Fig 3 Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I 4 Both the stones reach the bottom at different times and with different speeds

A river 500 meter wide is flowing at the rate of 2 m s A boat is sailing at a velocity of 10 m s with respect to water in the direction perpendicular to river How far from the point directly opposite to the starting point does the boat reach the opposite bank 1 40 m 2 80 m 3 100 m 4 120 m

16 Trajectory of particle in a projectile motion is given x as y x where x and y are in meter and 40 x axis is along horizontal y axis is along vertical The maximum height is 1y tanox 9 24 1 10 m 3 30 m 2 2 20 m 4 5 m

A car is moving on a straight road with uniform velocity 72 kmh 1 Suddenly the driver saw a child in the middle of road and applies brakes If he just able to save the child then reaction time of the driver is initial distance between car and child is 5 m and due to application of brakes uniform retardation of 50 ms 2 is developed 1 0 04 s 2 0 4 s 3 0 05 s 4 0 45 s

Which of the following graph represents uniform motion 1 S 3 t 2 4 S

A stone dropped from the top of the tower touches the ground in 4sec The h of the tower is about

5 Graph of versus x for a particle under motion is shown in figure where v is velocity and x is position Find the time taken by particle to move from x 4 m to x 12 m 1 m s 2 DAG x m

A boat which has speed of 5 kmh in still water crosses a river of width 1 km along the shortest possible path in 15 min The velocity of the river water is 1 1 kmh 1 2 3 kmh 1 3 4 kmh 1 4 41kmh

5 The table shows the distance covered in succes sive seconds by a body accelerated uniformly from rest Time interval s Distance cm I 2 II 6 III 10 IV 14 What is the speed of the body at the end of 4th sec a 4 cm sec b 8 cm sec c 14 cm sec d 16 cm sec

Figure shows the path A to C traced by a particle in xy plane B is a point on the path between x 10 cm and 50 cm such that the instantaneous particle velocity at B is the same in direction as the average particle velocity during the path A to B The x co ordinate of B is nearest to 1 16 cm Y in cm 30 30t A 20 10 2 22 cm M 10 20 30 40 3 50 X in cm 30 cm 4 44 cm

11 Trajectories are shown in figure for three kicked footballs Initial vertical horizontal velocity components are u and u respectively Ignoring air resistance choose the correct statement from Column II for the value of variable in Column I Column I A time of flight B u u C u D uu A C B Column II P greatest for A only Q greatest for C only R equal for A and B S equal for B and C

A stone is dropped from a height of 45 m on a horizontal level ground There is horizontal wind blowing due to which horizontal acceleration of the stone becomes 10 m s Take g 10 m s2 The time taken t by stone to reach the ground and the net horizontal displacement x of the stone from the time it is dropped and till it reaches the ground are respectively 1 t 3 s x 45 m 2 t 4s x 54 m 4 t 4s x 45 m 3 t 3s x 54 m

2 Example 25 A particle starts from rest and moves with a constant acceleration of 4 m s for 10 s then it moves under constant deceleration and stops in 20 s Find a the maximum velocity attained by the particle b the total distance traveled and c the distance distances from the origin when the particle is moving at half the maximum velocity