LFM Pure and Mechanics

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jee-main 2020 Q21 Free-fall and vertical drop View
A ball is dropped from the top of a 100 m high tower on a planet. In the last $\frac{1}{2}\,\mathrm{s}$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in $\mathrm{m\,s^{-2}}$) near the surface on that planet is $\underline{\hspace{1cm}}$
jee-main 2020 Q21 Inverse/implicit relationship between position and time View
The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x ^ { 2 } = a t ^ { 2 } + 2 b t + c$. If the acceleration of the particle depends on $x$ as $x ^ { - n }$, where $n$ is an integer, the value of $n$ is $\_\_\_\_$
jee-main 2020 Q21 Work-energy applied to launching or projecting objects View
A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force $F$ on the ball and moves horizontally a distance of 0.2 m while launching the ball, the value of $F$ (in N) is $\left( g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } \right)$
jee-main 2021 Q1 Acceleration then deceleration (two-phase motion) View
A car accelerates from rest at a constant rate $\alpha$ for some time after which it decelerates at a constant rate $\beta$ to come to rest. If the total time elapsed is t seconds, the total distance travelled is:
(1) $\frac { 4 \alpha \beta } { ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(2) $\frac { 2 \alpha \beta } { ( \alpha + \beta ) } t ^ { 2 }$
(3) $\frac { \alpha \beta } { 2 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
(4) $\frac { \alpha \beta } { 4 ( \alpha + \beta ) } \mathrm { t } ^ { 2 }$
jee-main 2021 Q2 Vertical projection from ground level View
A ball is thrown up with a certain velocity so that it reaches a height $h$. Find the ratio of the two different times of the ball reaching $\frac { h } { 3 }$ in both the directions.
(1) $\frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 }$
(2) $\frac { 1 } { 3 }$
(3) $\frac { \sqrt { 3 } - \sqrt { 2 } } { \sqrt { 3 } + \sqrt { 2 } }$
(4) $\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 }$
jee-main 2021 Q3 Acceleration then deceleration (two-phase motion) View
A scooter accelerates from rest for time $t _ { 1 }$ at constant rate $a _ { 1 }$ and then retards at constant rate $a _ { 2 }$ for time $t _ { 2 }$ and comes to rest. The correct value of $\frac { t _ { 1 } } { t _ { 2 } }$ will be :
(1) $\frac { a _ { 2 } } { a _ { 1 } }$
(2) $\frac { a _ { 1 } } { a _ { 2 } }$
(3) $\frac { a _ { 1 } + a _ { 2 } } { a _ { 1 } }$
(4) $\frac { a _ { 1 } + a _ { 2 } } { a _ { 2 } }$
jee-main 2021 Q3 Force-to-acceleration and resulting kinematics View
A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F _ { 0 } \left[ 1 - \left( \frac { t - T } { T } \right) ^ { 2 } \right]$ where $F _ { 0 }$ and $T$ are constants. The force acts only for the time interval $2 T$. The velocity $v$ of the particle after time $2 T$ is:
(1) $\frac { 2 F _ { 0 } T } { M }$
(2) $\frac { F _ { 0 } T } { 2 M }$
(3) $\frac { 4 F _ { 0 } T } { 3 M }$
(4) $\frac { F _ { 0 } T } { 3 M }$
jee-main 2021 Q22 Penetration and deceleration to rest View
A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of the bullet before hitting the wood is $10 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and, it slows down with uniform deceleration, then the magnitude of effective retarding force on the bullet is $x \mathrm {~N}$. The value of $x$ to the nearest integer is
jee-main 2022 Q1 Distance in successive equal time intervals View
A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in $t$ s, the distance travelled by the toy in the next $t$ s will be:
(1) 10 m
(2) 20 m
(3) 30 m
(4) 40 m
jee-main 2022 Q2 Vertical projection from ground level View
A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height $h$. Find the ratio of the times in which it is at height $\frac { h } { 3 }$ while going up and coming down respectively.
(1) $\frac { \sqrt { 2 } - 1 } { \sqrt { 2 } + 1 }$
(2) $\frac { \sqrt { 3 } - \sqrt { 2 } } { \sqrt { 3 } + \sqrt { 2 } }$
(3) $\frac { \sqrt { 3 } - 1 } { \sqrt { 3 } + 1 }$
(4) $\frac { 1 } { 3 }$
jee-main 2022 Q3 Two bodies meeting or catching up View
Two balls $A$ and $B$ are placed at the top of 180 m tall tower. Ball $A$ is released from the top at $t = 0 \mathrm {~s}$. Ball $B$ is thrown vertically down with an initial velocity $u$ at $t = 2 \mathrm {~s}$. After a certain time, both balls meet 100 m above the ground. Find the value of $u$ in $\mathrm { m } \mathrm { s } ^ { - 1 }$. [use $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$]
(1) 10
(2) 15
(3) 20
(4) 30
jee-main 2022 Q4 Deceleration and Stopping Distance on a Horizontal Surface View
A block of mass 10 kg starts sliding on a surface with an initial velocity of $9.8 \mathrm {~ms} ^ { - 1 }$. The coefficient of friction between the surface and block is 0.5 . The distance covered by the block before coming to rest is :[use $\mathrm { g } = 9.8 \mathrm {~ms} ^ { - 2 }$ ]
(1) 9.8 m
(2) 4.9 m
(3) 12.5 m
(4) 19.6 m
jee-main 2022 Q21 Two bodies meeting or catching up View
A ball is projected vertically upward with an initial velocity of $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at $t = 0 \mathrm {~s}$. At $t = 2 \mathrm {~s}$, another ball is projected vertically upward with same velocity. At $t =$ $\_\_\_\_$ s, second ball will meet the first ball $\left( \mathrm { g } = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 } \right)$.
jee-main 2023 Q1 Relative velocity and observed length/time View
Two trains $A$ and $B$ of length $l$ and $4l$ are travelling into a tunnel of length $L$ in parallel tracks from opposite directions with velocities $108 \mathrm{~km~h}^{-1}$ and $72 \mathrm{~km~h}^{-1}$, respectively. If train $A$ takes 35 s less time than train $B$ to cross the tunnel then, length $L$ of tunnel is: (Given $L = 60l$)
(1) 1200 m
(2) 900 m
(3) 1800 m
(4) 2700 m
jee-main 2023 Q2 Braking and stopping distance View
For a train engine moving with speed of $20 \mathrm {~ms} ^ { - 1 }$, the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt { x } \mathrm {~ms} ^ { - 1 }$. The value of $x$ is $\_\_\_\_$ . (Assuming same retardation is produced by brakes)
jee-main 2023 Q3 Relative velocity and observed length/time View
A passenger sitting in a train $A$ moving at $90 \mathrm {~km} \mathrm {~h} ^ { - 1 }$ observes another train $B$ moving in the opposite direction for 8 s . If the velocity of the train $B$ is $54 \mathrm {~km} \mathrm {~h} ^ { - 1 }$, then length of train $B$ is:
(1) 120 m
(2) 320 m
(3) 80 m
(4) 200 m
jee-main 2023 Q21 Average speed over a composite journey View
A horse rider covers half the distance with $5 \mathrm{~m~s}^{-1}$ speed. The remaining part of the distance was travelled with speed $10 \mathrm{~m~s}^{-1}$ for half the time and with speed $15 \mathrm{~m~s}^{-1}$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7} \mathrm{~m~s}^{-1}$. The value of $x$ is $\_\_\_\_$.
jee-main 2024 Q2 Average speed over a composite journey View
A particle moving in a straight line covers half the distance with speed $6 \mathrm {~m} / \mathrm { s }$. The other half is covered in two equal time intervals with speeds $9 \mathrm {~m} / \mathrm { s }$ and $15 \mathrm {~m} / \mathrm { s }$ respectively. The average speed of the particle during the motion is :
(1) $10 \mathrm {~m} / \mathrm { s }$
(2) $8 \mathrm {~m} / \mathrm { s }$
(3) $9.2 \mathrm {~m} / \mathrm { s }$
(4) $8.8 \mathrm {~m} / \mathrm { s }$
jee-main 2024 Q3 Distance in successive equal time intervals View
A body travels 102.5 m in $\mathrm { n } ^ { \text {th} }$ second and 115.0 m in $( \mathrm { n } + 2 ) ^ { \text {th} }$ second. The acceleration is :
(1) $6.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(2) $12.5 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(3) $9 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(4) $5 \mathrm {~m} / \mathrm { s } ^ { 2 }$
jee-main 2024 Q21 Distance in successive equal time intervals View
The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $( t + 1 )$ s are 125 m and $50 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, respectively. The distance travelled by the particle in $( t + 2 ) ^ { \text {th} } \mathrm { s }$ is $\_\_\_\_$ m.
jee-main 2024 Q21 Distance in successive equal time intervals View
A body moves on a frictionless plane starting from rest. If $S_n$ is distance moved between $t = n-1$ and $t = n$ and $S_{n-1}$ is distance moved between $t = n-2$ and $t = n-1$, then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1 - \frac{2}{x}\right)$ for $n = 10$. The value of $x$ is $\_\_\_\_$.
jee-main 2025 Q2 Vertical projection (up or down) from a height View
Q2. A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t _ { 1 }$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t _ { 2 }$. Time required to reach the ground, if it is dropped from the top of the tower, is :
(1) $\sqrt { t _ { 1 } t _ { 2 } }$
(2) $\sqrt { t _ { 1 } + t _ { 2 } }$
(3) $\sqrt { t _ { 1 } - t _ { 2 } }$
(4) $\sqrt { \frac { t _ { 1 } } { t _ { 2 } } }$
jee-main 2025 Q2 Braking and stopping distance View
Q2. Two cars are travelling towards each other at speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of $2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The distance between them when they come to rest is :
(1) 200 m
(2) 100 m
(3) 50 m
(4) 25 m
jee-main 2025 Q3 Distance in successive equal time intervals View
Q3. A body travels 102.5 m in $\mathrm { n } ^ { \text {th } }$ second and 115.0 m in $( \mathrm { n } + 2 ) ^ { \text {th } }$ second. The acceleration is :
(1) $6.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(2) $12.5 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(3) $9 \mathrm {~m} / \mathrm { s } ^ { 2 }$
(4) $5 \mathrm {~m} / \mathrm { s } ^ { 2 }$
jee-main 2025 Q3 Acceleration then deceleration (two-phase motion) View
Q3. A train starting from rest first accelerates uniformly up to a speed of $80 \mathrm {~km} / \mathrm { h }$ for time $t$, then it moves with a constant speed for time $3 t$. The average speed of the train for this duration of journey will be (in $\mathrm { km } / \mathrm { h }$ ) :
(1) 40
(2) 80
(3) 30
(4) 70

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