Kinematics Questions and Answers

An object of mass 10 kg is projected from ground with speed 40 m s at an angle 60 with horizontal The rate of change of momentum of object one second after projection in SI unit is Take g 9 8 m s 1 73 3 176 2 98 4 140

A body moves along x axis such that it s position is given by x is in seconds Identify correct options St 61 2 x is in meter t b Xmax a The smallest value of x during the motion is x 2 c At t 2 body changes it s direction of motion from ve x axis to ve x axis d At t 3 direction of motion changes from ve x axis to ve x axis 20 dation BY Where V is it s velocity at any

A particle is projected from ground at an angle wi horizontal with speed u The ratio of radius 0 curvature of its trajectory at point of projection radius of curvature at maximum height is 1 1 sin ecose 2 cos 0 3 1 sin 0 1

Projectile A particle is projected at angle 0 with horizontal from ground The slop m of the trajectory of the particle varies with time t as 1 m m 2 t f n m avo 3 m wol S 8

63 A particle accelerates from rest at a constant rate for some time and attains a velocity of 8 m Afterwards it decelerates with the constant rate and comes to rest If the total time taken is 4 secon the ratio of the distances travelled during acceleration and during deceleration is 4 1 3 2 2 1 1 1 1 3 1 2

Two masses m and 2m are connected by a string passing over a pulley fixed at the top of an inclined plane The first mass moves vertically downwards drawing the second up the incline If the angle of inclination is e and the coefficient of friction is u the acceleration of the system is less than it would be if the plane were smooth by an amount 1 2 g 3 1 2 sine g 3 2 4 2 3 2 3 sin eg g cose

Two particles A and B start moving with velocitie 20 m s and 30 2 m s along x axis and at an angl 45 with x axis respectively in xy plane from origin The relative velocity of Bw r t A 1 101 30 m s 2 30 10 m s 3 301 20 21 m s 4 30 5 Mpa

A ball is projected from ground at angle 0 with the horizontal After t 1 s it is moving at 45 with the horizontal and after t 2 second it is moving horizontally What is speed of projection of ball g 10 m s 10 2 m s O 10 3 m s 20 m s 10 5 m s

An object moves along the x axis according to the equation x 2 80 2 00 3 00 where x is in meters and t is in seconds a Determine the average speed between t 2 80 s and t 4 10 s m s b Determine the instantaneous speed at t 2 80 s m s Determine the instantaneous speed at t 4 10 s m s c Determine the average acceleration between t 2 80s and t 4 10 s m s d Determine the instantaneous acceleration at t 2 80 s mys Determine the instantaneous acceleration at t 4 10 s m s

Q is ahead of P by 350 m A car A is travelling along a straight level road with a uniform speed of 60 km h It is followed by another car B which is travelling uniformly at 70 km h When the distance between them is 2 5 km the car B decelerates at 20 km h Where will B catch up with A

A chain of mass m 4 kg and length 2 m rests on a rough horizontal surface such that some part of it hangs vertically when a small jerk is given the chain starts sliding down all by itself if the work done by friction till the chain slides of completely is 7 5 J then fraction of chain hanging initially is A 1 3 B 2 3 C 112 LD 14

For a particle projected from horizontal surface the ratio of range to maximum height reached is 0 is angle of projection with vertical 1 4 tane 3 tan 0 4 24cote R u jin20 cot 0 4 4 g 4 sin g

Question No 8 Single Correct A A A rocket is launched upward with an acceleration of 5 m s2 initial velocity is zero after 30 seconds its fuel is finished then find total time taken t it to reach the maximum height from ground 30 seconds 60 seconds 45 seconds 90 seconds Marks 4 00

Two spherical bodies having masses M and 3 M and radii r and 4r respectively are released in free space from rest such that the initial separation between their centres is 13 r If only force is gravitational attraction the distance covered by the smaller body just before collision is 1 6r 2 2r 3 13r 4 4 39r

8 A block of mass 10kg is initially at rest on a horizontal rough surface At a time t 0 a time dependent force F acts on it horizontally as shown in the figure Force F stops acting at t 7 seconds Consider that coefficient of static and kinetic friction both are equal to 0 5 and g 10 ms 2 10kg F N 100 40 I 1 7 t s 1 mv2 2 30 110x60x60 a Maximum kinetic energy acquired by the block is 125 J b Maximum kinetic energy acquired by the block is 50 J c Total time for which the block is moving with non zero velocity is 5 4 s d Total time for which the block is moving with non zero velocity is 7 4 s

A body moves from x 1 to x 4 and then to x 4 Which of the following is correct 1 Its displacement is zero 2 The distance covered by it is 5 units 3 Its displacement is 3 4 Distance covered by it is 9 units

7 Find the compression in the spring if the system shown below is in equilibrium 1 3 0 mg m mg cos 0 k M k voor 2 pmm Smooth mg sin cose k 4 Zero

1 4 particle is moving along a straight line The distance traveled from the starting position of th e particle 3 seconds later is 180 cm and the distance traveled in the next 5 seconds is 220 cm W hat will be the velocity of the particle after 9 seconds

A particle of mass m penetrates a medium at a speed to where it experiences a resistance proportional to the square of its speed with constant of proportionality k 0 Gravity may be ignored a What is the speed of the bullet as a function of position within the medium Use the initial condition v to at x 0 b Using the initial conditions v vo and x 0 at t 0 show that kvot 1 1

SolveLancer Test When an object projected vertically up from top of the building then its average velocity is 10 m s and it took 4 sec to reach the ground Find the difference between average speed and magnitude of average velocity SolveLancer Test a 1 5 m s b 2 5 m s c 2 m s d 5 m s

A car moving with a velocity of 10 m s can be stopped by the application of a constant force Fin a distance of 20m If the velocity of the car is 30 m s It can be stopped by this force in 120m 3 3 60 m 1 2 20 m 4 180 m

A staircase consists of five steps each 20 cm high and 20 cm wide If horizontal velocity of a ball is sufficient to fall it from top stair to bottom stair directly then the time taken by the ball to reach at bottom stair will be nearly 1 0 2 s 2 0 3 s 3 0 45 s 4 0 8 s In 0 1 If hall hits the edge of bottom stair then

The velocity of the car is expressed as V x 4x 3 3 and its time as t x 2x 5 Create a function model about the distance travelled of the car To solve the problem follow these steps a State the function model representing the velocity of the car b State the function model expressing the time lapse of the car c Recall the formula in finding the velocity of a moving object with respect to distance and time Derived a formula of distance from that formula d Create the function model for the distance travelled by the car Simply state your answer in a more comprehensible function model

irection ater in 3 in 1 1 city of A 1 24 J 2 48 J 3 56 J 4 64 J A block of mass 5 kg is placed on rough horizontal surface of 0 5 An external force F 50 N is acting on it at an angle of 37 above the horizontal The work done against friction when block cover 10 m distance along horizontal is 1 100 J 3 400 J 2 200 J 4 500 J

If a body covers first half of its journey with uniform speed v and the second hal of the journey with uniform speed v the the average speed is 1 2 1 V V 2 V V2 2 2 V V2 1 V V2 1 4 V V

ALLEN 4 The minimum energy required to launch a m kg 14 ma satellite from the earth s surface in circular orbit at an altitude 2R where R is the radius of earth is 1 mgR 2 mgR 4 mgR 5 3 mgR f f far and Raffront 1 mgR 3 mgR 2 mgR 4 mgR

Q 1 Q 30 Carry ONE mark each The two vectors P i q i j 2 are a related by a rotation c related by an inversion A 3 x 3 matrix has b related by a reflection through the xy pla d not linearly independent

The drawing shows a top view of a frictionless horizontal surface where there are two springs with particles of mass m and m attached to them Each spring has a spring constant of 1200 N m The particles are pulled to the right and then released from the positions shown in the drawing How much time passes before the particles are side by side for the first time na at x 0m if m 3 kg and m 27 kg If time is sec fill n in OMR sheet 80 Immo m mm m mo m Position of unstrained spring x 0

mass 25 kg rests on a horizontal floor u 0 2 It is attached by a 5m long horizontal rope to a peg fixed on floor The block is pushed along the ground with an initial velocity of 10 m s so that it moves in a circle around the peg Choose the correct statement s A Magnitude of tangential acceleration of the block is 2 m s B Speed of the block at time t 1 sec is 8 m s C Time when tension in rope becomes zero is 5 sec D Friction force acts towards centre of the circle 5m

A particle with an initial velocity vi enters a region with an electric field Ej and a magnetic field Bj The trajectory of the particle will a be an ellipse c be a helix with constant pitch b be a cycloid d not be confined to any plane

A solid hemisphere rests in equilibrium on a rough ground and against a smooth wall The curved surface touches the wall and the ground The angle of inclination of the circular base to the horizontal is 30 Find minimum coefficient of friction required between ground and hemisphere Fill 32 in OMR sheet

A ball is projected from point O on the ground It hits a smooth vertical wall AB at a height h and rebounds elastically The ball finally lands at a point C on the ground During the course of motion the maximum height attained by the ball is H E if OA 02 27134 OC a Find the ratio b Find the magnitude of average acceleration of the projectile for its entire course of flight if it was projected at an angle of 45 to the

Two balls are dropped from the top of a high tower wi time interval of t second where to is smaller than the time taken by the first ball to reach the floor which is perfectly inelastic The distance S between the two balls plotted against the time lapse t from the instant of dropping the second ball is best represented by

Note You anamping queron Answer A ball is dropped from a tower of height 30 0 m If the terminal speed of the ball is 25 0 m s then calculate the time taken by the ball to hit the ground a 2 67 s b 3 58 s c 2 47 s d 5 54 s Subject Test Submit

2 5 of 90 Two cars are travelling in the same direction with a velocity of 60 kmph They are separated by a distance of 5 km A truck moving in opposite direction meets the two cars in a time interval of 3 minute The velocity of the truck is in kmph 20 30 You marked

A platform is moving with velocity V m s in x direction A man starts moving on the platform with velocity 2V in x direction After reaching the right end he returns ba to the initial point In the whole journey his speed is remain constant and equal to 2 Now match the columns below COLUMN 1 1 What is the speed of the man with respect to earth while going in x direction 2 What is the speed of the man with respect to earth while returning back 3 What is the displacement of the particle with respect to earth 4 What is the displacement of the man with respect to platform 5 Find time at which its displacement with respect to earth will be maximum 2V A V D L G L 2V COLUMN 11 B 2V E 2L H L V C 3V F Zero

A locomotive of mass m starts moving with velocity v a s where a is constant s is distance traversed The total work done by all the forces acting on the locomotive during first t sec 1 4 B ma t 4 A ma 1 4 2 C ma ma 412 D 1ma4t 16 force actin

6 A particle starts from rest accelerates at 2 ms 2 for 10 s and then goes for constant speed for 30 s and then decelerates till it stops after next What is the distance travelled 2 at 4 ms by it a 750 m b 800 m c 700 m d 850 m

figure shown car A is travelling due north and car B is traveling due east They collide and stick to each other Here 1 2 3 4 ossible direction of motion of cars Which is most likely 1 2 4 W E

A particle is projected with velocity vo along x axis A damping force is acting on the particle which is proportional to the square of the distance from the origin i e ma ax The distance at which the particle stops 3 H A B 200 3x 3v 2a 3 2 D

A particle moves in a straight line and its position x at time t is given by x 2 t Its acceleration is given by 2 1 X 3 1 1 4x 2 1 4 2

A small boy is throwing a ball towards a wall 6 m in front of him He releases the ball at a height of 1 4 m from the ground The ball bounces from the wall at a height of 3m rebounds from the ground and reaches the boy s hand exactly at the point of release Assuming the two bounces one from the wall and the other from the ground to be perfectly elastic how far ahead of the boy did the ball bounce from ground 2013 A 1 5 m C 3 5 m B 2 5 m D 4 5 m

SINGLE CORRECT ANSWER TYPE A body of mass m is lifted from ground by a force which varies with height h as F 2 1 bh mg here b is constant Work done by this force over the first half distance of the ascent of body A 5mg 2b Fricuse B 3mg 8b C 3mg 4b D 10 mgb

5 A train of length 300 m travelling at 30 m s 1 crosses another train of length 200 m travelling at 20 m s 1 in opposite direction Time taken by first train to pass the second train is 1 10 s 2 30 s 3 50 s 4 2 s

A particle is projected up with an initial velocity of 80ft sec The ball will be at a height of 96 ft from the ground after given g 32 82 b Only at 3 0 sec d After 1 and 2 sec 2 0 and 3 0 sec c Only at 2 0 sec

Objects A and B each of mass m are connected by a light in extensible cord They are constrained to move on a friction less ring in a vertical plane as shown in fig The objects are released from rest at the positions shown The tension in the cord just after released will be B mg A mg C

A monkey of mass 40 kg climbs a rope Fig 1 58 which can stand a maximum tension of 600 N In which of the following cases will the rope break The monkey a climbs up with an acceleration of 6m s 2 b climbs down with acceleration of 4 m s a an c climbs up with a uniform speed of 5 m s 1 Fig 1 58 d falls down the rope nearly freely under gravity ignore the mass of the rope NCERT Ans a T 400 240 T 640 N b 400 T 160 T 240 N c T 400 N d T 0 The rope will break in case a

In the figure shown the masses of each of the pulley disc is m They were at rest All the threads are light and inextensible Now the thread is cut at A Denoting the acceleration of the discs as a a2 a3 a4 respectively match the correct value of acceleration v thereafter List I 1 11 a2 III a3 IV a4 a List II P Q R S T U I R II S III T IV T OI R II S III R IV R OI U II T III U IV U OI R II Q III R IV R 0 m s 10 m s 60 7 m s 90 7 m s 4 m s 2 m s www A 2 3 A

2 The angle of inclination of an inclined plane is 60 coefficient of friction between 10 kg body and its surface is 0 2 the acceleration of the body down the inclined plane in m s is g 10 m s 1 5 66 3 7 66 2 6 66 4 Zero

Find out the magnitude of resultant vector of 7 4N and 3N force 1 7 N 3 5 N W 4N 45 45 S 2 6 N 4 10 N 3N E 1 7 N 3 5 N W 4N 45 N S 2 4