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

## Mathematics

Kinematics

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Q 1. A river is flowing from west to east at a speed of 5 metres per minute, A man on the south bank of the river, capable of swimming at 10 metres per minute in still water, wants to swim across the river in the shortest time. He should swim in a direction

due north

B

{tex} 30 ^ { \circ } {/tex} east of north

C

{tex} 30 ^ { \circ } {/tex} west of north

D

{tex} 60 ^ { \circ } {/tex} east of north

##### Explanation

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Q 2. A boat which has a speed of {tex} 5 \mathrm { km } / \mathrm { hr } {/tex} in still water crosses a river of width {tex} 1 \mathrm { km } {/tex} along the shortest possible path in {tex}15{/tex} minutes. The velocity of the river water in {tex} \mathrm { km } / \mathrm { hr } {/tex} is

A

{tex}1{/tex}

{tex}3{/tex}

C

{tex}4{/tex}

D

{tex} \sqrt { 41 } {/tex}

##### Explanation

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Q 3. In 1.0{tex}\mathrm { s }{/tex} , a particle goes from point A to point B , moving in a semicircle of radius 1.0{tex}\mathrm { m }{/tex} (see Figure). The magnitude of the average velocity

A

{tex} 3.14 \mathrm { m } / \mathrm { s } {/tex}

{tex} 2.0 \mathrm { m } / \mathrm { s } {/tex}

C

{tex} 1.0 \mathrm { m } / \mathrm { s } {/tex}

D

Zero

##### Explanation

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Q 4. The velocity-displacement graph of a particle moving along a straight line is shown

The most suitable acceleration-displacement graph will be

B

C

D

##### Explanation

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Q 5. Consider a disc rotating in the horizontal plane with a constant angular speed m about its centre O. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y-z plane and is same for both pebbles With respect to the disc. Assume that (i) they land back on the before the disc has completed 1/8 rotation, (ii) their range is less than half the disc radius, and (iii) {tex} \omega {/tex} remains constant throughout. Then

A

{tex} P {/tex} lands in the shaded region and {tex} Q {/tex} in the unshaded region.

B

{tex} P {/tex} lands in the unshaded region and {tex} Q {/tex} in the shaded region.

Both {tex} P {/tex} and {tex} Q {/tex} land in the unshaded region.

D

Both {tex} P {/tex} and {tex} Q {/tex} land in the shaded region.

##### Explanation

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Q 6. A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is {tex} 1 \mathrm { m } {/tex} long and takes {tex} 1 \mathrm { s } {/tex}. There is a pit on the road {tex} 11 \mathrm { m } {/tex} away from the starting point. The drunkard will fall into the pit after

{tex} 29 \mathrm { s } {/tex}

B

{tex} 21 \mathrm { s } {/tex}

C

{tex} 37 \mathrm { s } {/tex}

D

{tex} 31 \mathrm { s } {/tex}

##### Explanation

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Q 7. The distance travelled by a particle in a straight line motion is directly proportional to {tex} t ^ { 1 / 2 } , {/tex} where {tex} t = {/tex} time elapsed. What is the nature of motion?

A

Increasing acceleration

B

Decreasing acceleration

C

Increasing retardation

Decreasing retardation

##### Explanation

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Q 8. A body is released from the top of a tower of height {tex} H \mathrm { m } {/tex}. After {tex} 2 \mathrm { s } {/tex} it is stopped and then instantaneously released. What will be its height after next {tex} 2 \mathrm { s } {/tex} ?

A

{tex} ( H - 5 ) \mathrm { m } {/tex}

B

{tex} ( H - 10 ) \mathrm { m } {/tex}

C

{tex} ( H - 20 ) \mathrm { m } {/tex}

{tex} ( H - 40 ) \mathrm { m } {/tex}

##### Explanation

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Q 9. The location of a particle is changed. What can we say about the displacement and distance covered by the particle?

Both cannot be zero

B

One of the two may be zero

C

Both must be zero

D

Both must be equal

##### Explanation

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Q 10. Four persons are initially at the four corners of a square side is equal to {tex} d {/tex}. Each person now moves with a uniform speed {tex} V {/tex} in such a way that the first moves directly towards the second , the second directly towards the third, the third directly towards the fourth, and the fourth directly towards the first. The four persons will meet after a time equal to

{tex} d / V {/tex}

B

{tex} 2 d / 3 V {/tex}

C

{tex} 2 d / \sqrt { 3 } V {/tex}

D

{tex} d / \sqrt { 3 } V {/tex}

##### Explanation

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Q 11. A particle is projected at an angle of elevation {tex} \alpha {/tex} and after {tex} t {/tex} second, it appears to have an angle of elevation {tex} \beta {/tex} as seen from point of projection. The initial velocity will be

A

{tex} \frac { \mathrm { g } t } { 2 \sin ( \alpha - \beta ) } {/tex}

{tex} \frac { \mathrm { g } t \cos \beta } { 2 \sin ( \alpha - \beta ) } {/tex}

C

{tex} \frac { \sin ( \alpha - \beta ) } { 2 g t } {/tex}

D

{tex} \frac { 2 \sin ( \alpha - \beta ) } { \operatorname { gt } \cos \beta } {/tex}

##### Explanation

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Q 12. A plane flying horizontally at {tex} 100 \mathrm { ms } ^ { - 1 } {/tex} releases an object which reaches the ground in {tex} 10 \mathrm { s } {/tex}. At what angle with horizontal it hits the ground?

A

{tex} 55 ^ { \circ } {/tex}

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

C

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

D

{tex} 75 ^ { \circ } {/tex}

##### Explanation

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Q 13. A body of mass {tex} m {/tex} is projected horizontally with a velocity {tex} v {/tex} from the top of a tower of height {tex} h {/tex} and it reaches the ground at a distance {tex} x {/tex} from the foot of the tower. If a second body of mass {tex} 2 \mathrm { m } {/tex} is projected horizontally from the top of a tower of height {tex} 2 h , {/tex} it reaches the ground at a distance {tex} 2 x {/tex} from the foot of the tower. The horizontal velocity of the second body is

A

{tex}v{/tex}

B

{tex} 2 v {/tex}

{tex} \sqrt { 2 } v {/tex}

D

{tex} v / 2 {/tex}

##### Explanation

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Q 14. Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation {tex} \alpha = 30 ^ { \circ } , \beta {/tex} {tex}= 60 ^ { \circ } , {/tex} respectively Fig. The shots strike an object simultaneously at the same point. If {tex} a = 30 \sqrt { 3 } \mathrm { m } {/tex} is the horizontal distance of the object from the cliff, then the height {tex} h {/tex} of the cliff is

A

{tex} 30 \mathrm { m } {/tex}

B

{tex} 45 \mathrm { m } {/tex}

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

D

{tex} 90 \mathrm { m } {/tex}

##### Explanation

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Q 15. The ratio of the distance carried away by the water current, downstream, in crossing a river, by a person, making same angle with downstream and upstream is {tex} 2: 1 . {/tex} The ratio of the speed of person to the water current cannot be less than

{tex} 1 / 3 {/tex}

B

{tex} 4 / 5 {/tex}

C

{tex} 2 / 5 {/tex}

D

{tex} 4 / 3 {/tex}