Question 1 :
A particle experiences a fixed acceleration for 6s after starting from rest. It covers a distance of s<sub>1</sub>in first two seconds, s<sub>2</sub>in the next 2 seconds and s<sub>3</sub>in the last 2 seconds then s<sub>3</sub>: s<sub>2</sub>: s<sub>1</sub>is
Question 2 :
A particle starts from the origin at {tex} t = 0 {/tex} s with a velocity of {tex} 10.0 \hat { j } \mathrm { m } / \mathrm { s } {/tex} and moves in the {tex} x - y {/tex} plane with a constant acceleration of {tex} ( 8.0 \hat { i } + 2.0 \hat { j } ) \mathrm { ms } ^ { - 2 } {/tex} At a time when {tex} x {/tex} -coordinate of the particle {tex} 16 \mathrm { m } , {/tex}What is the y-coordinate of the particle at that time?
Question 3 :
The velocity of a particle that moves in the positive x-direction varies with its position(x) as shown in Fig.2.21. Its acceleration x = 6m is <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d5803ca40fda93533ee5b0e" />
Question 4 :
A ball thrown upward from the top of tower with speed <em>v</em> reaches the ground in <em>t</em><sub>1</sub> second. If this ball is thrown downward from the top of the same tower with speed <em>v</em> it reaches the ground in <em>t</em><sub>2</sub> second. In what time the ball shall reach the ground if it is allowed to fall freely under gravity from the top of the tower?
Question 5 :
A tank moves uniformly along x-axis. It fires a shot from origin at an angle of 30<sup>0</sup> with horizontal while moving along positive x-axis and the second shot is also fired similarly except that the tank moves along negative x-axis. If the respective range of the shot are 250 m and 210m along x-axis, then the initial velocity values are<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e5bab5f89758f2d4ef59' height='119' width='144' >
Question 6 :
Which of the following options is correct for the object having a straight line motion represented by the following graph<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5dc28896b27c0666ff0b36d0.jpg" />
Question 7 :
A particle is thrown with a speed of {tex}12 \mathrm { m } / \mathrm { s } {/tex} at an angle {tex} 60 ^ { \circ } {/tex} with the horizontal. The time interval between the moments when its speed is {tex} 10\mathrm { m } / \mathrm { s } {/tex} is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 8 :
{tex}\mathrm {Assertion} \quad {/tex} :A body having non-zero acceleration can have a constant velocity.<br> {tex}\mathrm {Reason} \quad {/tex} :Acceleration is the rate of change of velocity.
Question 9 :
A swimmer wishes to cross a 800{tex} \mathrm { m } {/tex} wide river flowing at {tex}6 \mathrm { km } / \mathrm { hr } {/tex} . His speed with respect to water is {tex}4 \mathrm { km } / \mathrm { hr } {/tex} . He crosses the river in shortest possible time. He is drifted downstream on reaching the other bank by a distance of
Question 10 :
A stone is projected from the ground with velocity {tex} 50 \mathrm { m } / \mathrm { s } {/tex} at an angle of {tex} 30 ^ { \circ } . {/tex} It crosses a wall after {tex} 3 \mathrm { sec } {/tex}. How far beyond the wall the stone will strike the ground {tex} \left( g = 10 \mathrm { m } / \mathrm { sec } ^ { 2 } \right) {/tex}
Question 11 :
A particle starts moving from the position of rest under a constant acceleration. It travels a distance {tex} x {/tex} in the first 10{tex} \mathrm { s } {/tex} and distance {tex} y {/tex} in the next {tex} 10 \mathrm { s } , {/tex} then
Question 12 :
An aeroplane drops a parachutist. After covering a distance of 40 m, he opens the parachute and retards at 2 ms<sup>-2</sup>. If he reaches the ground with a speed of 2 m<sup>-1</sup>, he remains in the air for about
Question 13 :
The maximum height attained by a projectile is increased by 5%, keeping the angle of projection constant. The corresponding percentage increase in horizontal range will be
Question 14 :
The projectiles {tex} A {/tex} and {tex} B {/tex} thrown with velocities {tex} v {/tex} and {tex} \frac { v } { 2 } {/tex} have the same range. If {tex} B {/tex} is thrown at an angle of {tex} 15 ^ { \circ } {/tex} to the horizontal, {tex} A {/tex} must have been thrown at an angle
Question 15 :
A body is projected at an angle {tex} \alpha {/tex} with velocity 10{tex} \mathrm { m } / \mathrm { s } {/tex} . Its direction of motion makes an angle of {tex} \alpha / 2 {/tex} from horizontal after {tex} t {/tex} s {tex} \left( g = 10 \mathrm { ms } ^ { - 2 } \right) , {/tex} where {tex} t {/tex} is.
Question 16 :
A projectile has the same range {tex} R {/tex} for two angles of projection. If {tex} T _ { 1 } {/tex} and {tex} T _ { 2 } {/tex} be the times of flight in the two cases, then {tex} R {/tex} is
Question 17 :
A particle is thrown with a speed of 12 m/s at an angle 60<font face="Symbol">°</font> with the horizontal. The time interval between the moments when its speed is 10 m/s is (<em>g</em> = 10 m/s<sup>2</sup>)
Question 18 :
A ball is thrown upwards. Its height varies with time as shown in figure. If the acceleration due to gravity is 10 m/s<sup>2</sup>, then the height h is-<br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e75e74fb5f89758f2d4f0db' height='117' width='212' >
Question 19 :
A horizontal wind is blowing with a velocity towards north-east. A man starts running towards north with acceleration {tex} a {/tex} . The time, after which man will feel the wind blowing towards east, is
Question 20 :
A driver applies the brakes on seeing traffic signal 400 m ahead. At the time of applying the brakes the vehicle was moving with 15 m s<sup>–1</sup> and retarding with 0.3 m s<sup>–2</sup>. The distance of the vehicle after 1 minute from the traffic light is
Question 21 :
From a canon mounted on a wagon at height H from ground, a shell is fired horizontally with a velocity {tex}v_{0}{/tex} with respect to canon. The canon and wagon has combined mass M and can move freely on the horizontal surface. The horizontal distance between shell and canon when the shell touches the ground is <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d58049841fcca588ca355f6" />
Question 22 :
A particle moves along {tex} x {/tex} -axis as {tex} x = 4 ( t - 2 ) + a ( t - 2 ) ^ { 2 } {/tex} Which of the following is true?
Question 23 :
A body falling for 2 seconds covers a distance {tex} S {/tex} equal to that covered in next second. Taking {tex} g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } , S = {/tex}
Question 24 :
A particle is projected with velocity {tex} v _ { 0 } {/tex} along {tex} x - {/tex}axis. The deceleration on the particle is proportional to the square of the distance from the origin i.e., {tex} a = \alpha x ^ { 2 } {/tex}. The distance at which the particle stops is
Question 25 :
{tex}\mathrm {Assertion} \quad {/tex} :An object can have constant speed but variable velocity.<br> {tex}\mathrm {Reason} \quad {/tex} :Speed is a scalar but velocity is a vector quantity.
Question 26 :
A ball is thrown vertically upwards from the ground. It crosses a point at the height of {tex}25{tex} \mathrm { m } {/tex} twice at an interval of {tex} 4 \mathrm { s } . {/tex} The ball was thrown with the velocity of {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 27 :
A pebble is thrown vertically upwards from a bridge with an initial velocity of {tex} 10 \mathrm { ms } ^ { - 1 } . {/tex} It strikes water after {tex} 5 \mathrm { s } . {/tex} The height of the bridge is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 28 :
A ball is dropped on the floor from a height of {tex} 10 \mathrm { m } {/tex}. It rebounds to a height of {tex} 2.5 \mathrm { m } {/tex}. If the ball is in contact with the floor for {tex} 0.01 \mathrm { sec } {/tex}, the average acceleration during contact is
Question 29 :
A body is moving from rest under constant acceleration and let {tex} S _ { 1 } {/tex} be the displacement in the first {tex} ( p - 1 ) {/tex} s and {tex} S _ { 2 } {/tex} be the displacement in the first {tex} p {/tex} s. The displacement in {tex} \left( p ^ { 2 } - p + 1 \right) ^ { \text { th } } {/tex} s will be
Question 30 :
A body is projected up with a speed {tex} 'u ^ { \prime } {/tex} and the time taken by it is {tex} T {/tex} to reach the maximum height {tex} H . {/tex} Pick out the correct<br>statement<br>
Question 31 :
A particle is projected from ground with velocity 40{tex} \sqrt { 2 } \mathrm { m } / \mathrm { s } {/tex} at {tex} 45 ^ { \circ } . {/tex} At time {tex} t = 2 \mathrm { s } : {/tex}
Question 32 :
A coin is dropped in a lift. It takes time {tex} t _ { 1 } {/tex} to reach the floor when lift is stationary. It takes time {tex} t _ { 2 } {/tex} when lift is moving up with constant acceleration, then
Question 33 :
One body is dropped, while a second body is thrown downward with an initial velocity of 1{tex} \mathrm { ms } ^ { - 1 } {/tex} simultaneously. The separation between these is 1.8{tex} \mathrm { m } {/tex} after a time
Question 34 :
A motorcyclist starts from the bottom of a slope of angle 45º to cross the valley <em>PR</em> as shown in the figure. The width of the valley is 90m and length of the slope is {tex}\text{80}\sqrt{2}{/tex}m. The minimum velocity at point <em>O</em> required to clear the valley will be <br> <img style='object-fit:contain' style="max-width:240px;" src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5f16bd8e4bec8070e4e14fa0"/>
Question 35 :
A shell fired from the ground is just able to cross in a horizontal direction the top of a wall {tex} 90{tex} \mathrm { m } {/tex} away and{tex} 45 \mathrm { m } {/tex} high. The direction of projection of the shell is
Question 36 :
A ball is dropped from the roof of a tower of height {tex} h {/tex} . The total distance covered by it in the last second of its motion is equal to the distance covered by it in first three seconds. The value of {tex} h {/tex} in meters is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 37 :
A particle is projected vertically upward with a speed of 100{tex} \mathrm { m } / \mathrm { s } {/tex} . The distance travelled by the particle in first fifteen seconds is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}
Question 38 :
The velocity time graph of a particle starting from rest from a point P is shown here. Particle will reach P again, after starting from P in time <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5d58038c41fcca588ca35539" />
Question 39 :
A particle is projected upwards with a velocity of 100 m/s at an angle of 37<font face="Symbol">°</font> with the vertical. The time when the particle will move perpendicular to its initial direction is (<em>g</em> = 10 m/s<sup>2</sup>, tan 53<font face="Symbol">°</font> = 4/3)
Question 40 :
{tex}\mathrm {Assertion} \quad {/tex} :The average speed of a body over a given interval of time is equal to the average velocity of the body in the same interval of time if a body moves in a straight line in one direction.<br>{tex}\mathrm {Reason} \quad {/tex} :Because in this case distance travelled by a body is equal to the displacement of the body.<br>
Question 41 :
The position of a particle is given by <br> \[ r = 3.0 t \hat { i } - 2.0 t ^ { 2 } \hat { j } + 4.0 \hat { k } \mathrm { m } \] Where {tex} t {/tex} is in seconds and the coefficients have the proper units for {tex} r {/tex} to be in metres. <br> What is the magnitude of velocity of the particle {tex} t = 2.0 \mathrm { s } ? {/tex}
Question 42 :
A particle located at {tex} x = 0 {/tex} at time {tex} t = 0 {/tex} , starts mov ing 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
Question 43 :
{tex}\mathrm {Assertion} \quad {/tex} :Rocket in flight is not an illustration of projectile.<br> {tex}\mathrm {Reason} \quad {/tex} :Rocket takes flight due to combustion of fuel and does not move under the gravity effect alone.
Question 44 :
A projectile is thrown horizontally from top of a building of height {tex}10 \mathrm { m } {/tex} with certain speed {tex} ( u ) {/tex} . At the same time another projectile is thrown from ground 10{tex} \mathrm { m } {/tex} away from the building with equal speed {tex} ( u ) {/tex} on the same vertical plane. If they collide after {tex} 2 s , {/tex} then choose the correct options.
Question 45 :
The displacement of a particle as a function of time is shown in the figure. The figure shows that<br><img style='object-fit:contain' src="https://data-screenshots.sgp1.digitaloceanspaces.com/5dc292feb27c0666ff0b37d1.jpg" />
Question 46 :
A car {tex} A {/tex} is travelling on a straight level road with a uniform speed of {tex} 60 \mathrm { km } / \mathrm { h } {/tex}. It is followed by another car {tex} B {/tex} which is moving with a speed of {tex} 70 \mathrm { km } / \mathrm { h } {/tex}. When the distance between them is {tex} 2.5 \mathrm { km } {/tex}, the car {tex} \mathrm { B } {/tex} is given a deceleration of {tex} 20 \mathrm { km } / \mathrm { h } ^ { 2 } {/tex}. After how much time will {tex} B {/tex} catch up with {tex} \mathrm { A } {/tex}
Question 47 :
The relation between time and distance is {tex} t = \alpha x ^ { 2 } + \beta x , {/tex} where {tex} \alpha {/tex} and {tex} \beta {/tex} are constants. The retardation is
Question 48 :
If rain drops are falling with velocity of {tex}12 \mathrm { m } / \mathrm { s } {/tex} at an angle of {tex} 30 ^ { \circ } {/tex} with the vertical. With what possible speed(s), a man should move in horizontal direction so that rain drops hit him at an angle of {tex} 45 ^ { \circ } {/tex} with the horizontal.
Question 49 :
A ball is thrown vertically upwards from the ground. It crosses a point at the height of 25 m twice at an interval of 4 second. The ball was thrown with the velocity of (<em>g</em> = 10 m/s<sup>2</sup>)
Question 50 :
A very broad elevator is going up vertically with a constant acceleration of 2{tex} \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} . At the instant when its velocity is 4{tex} \mathrm { m } / \mathrm { s } {/tex} a ball is projected from the floor of the lift with a speed of 4{tex} \mathrm { m } / \mathrm { s } {/tex} relative to the floor at an elevation of {tex} 30 ^ { \circ } . {/tex} The time taken by the ball to return the floor is {tex} \left( g = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) {/tex}