JEE Main

Explore popular questions from Kinematics for JEE Main. This collection covers Kinematics previous year JEE Main questions hand picked by experienced teachers.

Mathematics

Kinematics

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Q 1. The co-ordinates of a moving particle at any time {tex} t {/tex} are given by {tex} x = \alpha t ^ { 3 } {/tex} and {tex} y = \beta t ^ { 3 } . {/tex} The speed of the particle at time {tex} t {/tex} is given by

A

{tex} 3 t \sqrt { \alpha ^ { 2 } + \beta ^ { 2 } } {/tex}

{tex} 3 t ^ { 2 } \sqrt { \alpha ^ { 2 } + \beta ^ { 2 } } {/tex}

C

{tex} t ^ { 2 } \sqrt { \alpha ^ { 2 } + \beta ^ { 2 } } {/tex}

D

{tex} \sqrt { \alpha ^ { 2 } + \beta ^ { 2 } } {/tex}

Explanation

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Q 2. A ball is released from the top of a tower of height {tex} h {/tex} metre. It takes {tex} T {/tex} second to reach the ground. What is the position of the ball in {tex} T / 3 {/tex} second?

A

{tex} h / 9 {/tex} metre from the ground

B

{tex} 7 h / 9 {/tex} metre from the ground

{tex} 8 h / 9 {/tex} metre from the ground

D

{tex} 17 h / 18 {/tex} metre from the ground.

Explanation

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Q 3. The relation between time {tex} t {/tex} and distance {tex} x {/tex} is {tex} t = a x ^ { 2 } + b x {/tex} where {tex} a {/tex} and {tex} b {/tex} are constants. The acceleration is

{tex} - 2 a v ^ { 3 } {/tex}

B

{tex} 2 a v ^ { 2 } {/tex}

C

{tex} - 2 a v ^ 2{/tex}

D

{tex} 2 b v ^ { 3 } {/tex}

Explanation

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Q 4. Speeds of two identical cars are {tex} u {/tex} and {tex} 4 u {/tex} at a specific instant. If the same deceleration is applied on both the cars, the ratio of the respective distances in which the two cars are stopped from that instant is

A

1:1

B

1:4

C

1:8

1:16

Explanation

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Q 5. A particle is moving eastwards with a velocity of {tex} 5 \mathrm { m } / \mathrm { s } {/tex}. In {tex} 10 \mathrm { s } {/tex} the velocity changes to {tex} 5 \mathrm { m } / \mathrm { s } {/tex} northwards. The average acceleration in this time is (a) zero

A

Zero

{tex} \frac { 1 } { \sqrt { 2 } } \mathrm { ms } ^ { - 2 } {/tex} towards north-west

C

{tex} \frac { 1 } { \sqrt { 2 } } \mathrm { ms } ^ { - 2 } {/tex} towards north-east

D

{tex} \frac { 1 } { 2 } \mathrm { ms } ^ { - 2 } {/tex} towards north

Explanation

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Q 6. A parachutist after bailing out falls {tex} 50 \mathrm { m } {/tex} without friction. When parachute opens, it decelerates at {tex} 2 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} He reaches the ground with a speed of {tex} 3 \mathrm { m } / \mathrm { s } {/tex}. At what height, did he bail out?

{tex} 293 \mathrm { m } {/tex}

B

{tex} 111 \mathrm { m } {/tex}

C

{tex} 91 \mathrm { m } {/tex}

D

{tex} 182 \mathrm { m } {/tex}

Explanation

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Q 7. A projectile can have the same range {tex} R {/tex} for two angles of projection. If {tex} t _ { 1 } {/tex} and {tex} t _ { 2 } {/tex} be the time of flights in the two cases, then the product of the two time of flights is proportional to

A

{tex} 1 / R {/tex}

{tex} R {/tex}

C

{tex} R ^ { 2 } {/tex}

D

{tex} 1 / R ^ { 2 } {/tex}

Explanation

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Q 8. An automobile travelling with a speed of {tex} 60 \mathrm { km } / \mathrm { h } {/tex}, can brake to stop within a distance of {tex} 20 \mathrm { m } . {/tex} If the car is going twice as fast, i.e. {tex} 120 \mathrm { km } / \mathrm { h } {/tex}, the stopping distance will be

A

{tex} 20 \mathrm { m } {/tex}

B

{tex} 40 \mathrm { m } {/tex}

C

{tex} 60 \mathrm { m } {/tex}

{tex} 80 m {/tex}

Explanation

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Q 9. A projectile can have the same range {tex} R {/tex} for two angles of projection. If {tex} T _ { 1 } {/tex} and {tex} T _ { 2 } {/tex} be the time of flights in the two cases, then the product of the two time of flights is directly proportional to

A

{tex} 1 / R ^ { 2 } {/tex}

B

{tex} 1 / R {/tex}

{tex} R {/tex}

D

{tex} R ^ { 2 } {/tex}

Explanation

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Q 10. A particle located at {tex} x = 0 {/tex} at time {tex} t = 0 {/tex}, starts moving along the positive {tex} x {/tex} -direction with a velocity {tex} v {/tex} that varies as {tex} v = \alpha \sqrt { x } {/tex}. The displacement of the particle varies with time as

A

{tex} t ^ { 3 } {/tex}

{tex} t ^ { 2 } {/tex}

C

t

D

{tex} t ^ { 1 / 2 } {/tex}

Explanation

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Q 11. From a building two balls {tex} A {/tex} and {tex} B {/tex} are thrown such that {tex} A {/tex} is thrown upwards and {tex} B {/tex} downwards (both vertically). If {tex} v _ { \text {a } }\ and\ v _ { B } {/tex} are their respective velocities on reaching the ground, then

A

{tex} v _ { B } > v _ { A } {/tex}

{tex} v _ { A } = v _ { B } {/tex}

C

{tex} v _ { A } > v _ { B } {/tex}

D

their velocities depend on their masses.

Explanation

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Q 12. Which of the following statements is false for a particle moving in a circle with a constant angular speed?

A

The velocity vector is tangent to the circle.

The acceleration vector is tangent to the circle

C

the acceleration vector points to the centre of the circle

D

the velocity and acceleration vectors are perpendicular to each other.

Explanation

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Q 13. If a body looses half of its velocity on penetrating {tex} 3 \mathrm { cm } {/tex} in a wooden block, then how much will it penetrate more before coming to rest?

{tex} 1 \mathrm { cm } {/tex}

B

{tex} 2 \mathrm { cm } {/tex}

C

{tex} 3 \mathrm { cm } {/tex}

D

{tex} 4 \mathrm { cm } {/tex}

Explanation

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Q 14. A boy playing on the roof of a {tex} 10 \mathrm { m } {/tex} high building throws a ball with a speed of {tex} 10 \mathrm { m } / \mathrm { s } {/tex} at an angle of {tex} 30 ^ { \circ } {/tex} with the horizontal. How far from the throwing point will the ball be at the height of {tex} 10 \mathrm { m } {/tex} from the ground {tex} ? \left[ g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } , \sin 30 ^ { \circ } = \right. {/tex} {tex} \left. 1 / 2 , \cos 30 ^ { \circ } = \sqrt { 3 } / 2 \right] {/tex}

A

{tex} 5.20 \mathrm { m } {/tex}

B

{tex} 4.33 \mathrm { m } {/tex}

C

{tex} 2.60 m {/tex}

{tex} 8.66 \mathrm { m } {/tex}

Explanation

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Q 15. Two forces are such that the sum of their magnitudes is {tex} 18 \mathrm { N } {/tex} and their resultant is {tex} 12 \mathrm { N } {/tex} which is perpendicular to the smaller force. Then the magnitudes of the forces are

A

{tex} 12 \mathrm { N } , 6 \mathrm { N } {/tex}

{tex} 13 \mathrm { N } , 5 \mathrm { N } {/tex}

C

{tex} 10 \mathrm { N } , 8 \mathrm { N } {/tex}

D

{tex} 16 \mathrm { N } , 2 \mathrm { N } {/tex}

Explanation

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Q 16. A car moving with a speed of {tex} 50 \mathrm { km } / \mathrm { hr } , {/tex} can be stopped by brakes after at least {tex} 6 \mathrm { m } {/tex}. If the same car is moving at a speed of {tex} 100 \mathrm { km } / \mathrm { hr } {/tex}, the minimum stopping distance is

A

{tex} 12 \mathrm { m } {/tex}

B

{tex} 18 \mathrm { m } {/tex}

{tex} 24 \mathrm { m } {/tex}

D

{tex} 6 \mathrm { m } {/tex}

Explanation

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Q 17. A ball is thrown from a point with a speed {tex} v _ { 0 } {/tex} at an angle of projection {tex} \theta . {/tex} From the same point and at the same instant a person starts running with a constant speed {tex} v _ { 0 } / 2 {/tex} to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

yes, {tex} 60 ^ { \circ } {/tex}

B

yes, {tex} 30 ^ { \circ } {/tex}

C

{tex} \mathrm { no }, 30 ^ { \circ }{/tex}

D

yes, {tex} 45 ^ { \circ } {/tex}

Explanation

Yes, the person can catch the ball when horizontal velocity is equal to the horizontal component of ball's velocity , the motion of ball be only in vertical direction with respect to person for that , {tex}\frac{v_0}{2}=v_0cos \theta \space or\space \theta=60 \degree.{/tex}

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Q 18. If {tex} \vec { A } \times \vec { B } = \vec { B } \times \vec { A } , {/tex} then the angle between {tex} A {/tex} and {tex} B {/tex} is

{tex} \pi {/tex}

B

{tex} \pi / 3 {/tex}

C

{tex} \pi / 2 {/tex}

D

{tex} \pi / 4 {/tex}

Explanation

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Q 19. A body is at rest at {tex} x = 0 . {/tex} At {tex} t = 0 , {/tex} it starts moving in the positive {tex} x {/tex} -direction with a constant acceleration. At the same instant another body passes through {tex} x = 0 {/tex} moving in the positive {tex} x {/tex} -direction with a constant speed. The position of the first body is given by {tex} x _ { 1 } ( t ) {/tex} after time {tex} t {/tex} and that of the second body by {tex} x _ { 2 } ( t ) {/tex} after the same time interval. Which of the following graphs correctly describes {tex} \left( x _ { 1 } - x _ { 2 } \right) {/tex} as a function of time {tex} t {/tex} ?

A

B

D

Explanation

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Q 20. A car is travelling with linear velocity {tex} v {/tex} on a circular road of radius {tex} r . {/tex} If it is increasing its speed at the rate of ' {tex} ^ { \prime } a ^ { \prime } {/tex} {tex}meter{/tex} / {tex}sec^{2}{/tex}', then the resultant acceleration will be

A

{tex} \sqrt { \left\{ \frac { v ^ { 2 } } { r ^ { 2 } } - a ^ { 2 } \right\} } {/tex}

{tex} \sqrt { \left\{ \frac { v ^ { 4 } } { r ^ { 2 } } + a ^ { 2 } \right\} } {/tex}

C

{tex} \sqrt { \left\{ \frac { v ^ { 4 } } { r ^ { 2 } } - a ^ { 2 } \right\} } {/tex}

D

{tex} \sqrt { \left\{ \frac { v ^ { 2 } } { r ^ { 2 } } + a ^ { 2 } \right\} } {/tex}

Explanation

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Q 21. At the highest point of the path of a projectile, its

A

Kinetic energy is maximum

B

Potential energy is minimum

Kinetic energy is minimum

D

Total energy is maximum

Explanation

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Q 22. A body is projected horizontally from a height with speed 20 metres/sec. What will be its speed after 5 seconds {tex} (g = 10 \text { metres/sec } ^ { 2 } {/tex} )

54 metres/sec

B

20 metres/sec

C

50 metres/sec

D

70 metres/sec

Explanation

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Q 23. A projectile projected at an angle {tex} 30 ^ { \circ } {/tex} from the horizontal has a range {tex} R . {/tex} If the angle of projection at the same initial velocity be {tex} 60 ^ { \circ } , {/tex} then the range will be

{tex} R {/tex}

B

{tex} 2 R {/tex}

C

{tex} R / 2 {/tex}

D

{tex} R ^ { 2 } {/tex}

Explanation

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Q 24. A small body of mass {tex} m {/tex} slides down from the top of a hemisphere of radius {tex} r . {/tex} The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is

A

{tex} \frac { 3 } { 2 } r {/tex}

{tex} \frac { 2 } { 3 } r {/tex}

C

{tex} \frac { 1 } { 2 } g t^2 {/tex}

D

{tex} \frac { v ^ { 2 } } { 2 g } {/tex}

Explanation

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Q 25. A boy walks to his school at a distance of {tex} 6 \mathrm { km } {/tex} with constant speed of {tex} 2.5 \mathrm { km }/ hour {/tex} and walks back with a constant speed of {tex} 4 \mathrm { km }/ hour {/tex}. His average speed for round trip expressed in {tex} \mathrm { km }/ hour {/tex} , is

A

{tex} 24 / 13 {/tex}

{tex} 40 / 13 {/tex}

C

{tex}3{/tex}

D

{tex} 1 / 2 {/tex}