LFM Pure and Mechanics

iran-konkur 2023 Q47 Two bodies meeting or catching up View

47. Car A moves at a constant speed of $8\,\dfrac{\text{m}}{\text{s}}$ along a straight path, and car B moves behind it at a constant speed of $20\,\dfrac{\text{m}}{\text{s}}$ in the same direction. When the distance between them decreases to 46 meters, car A begins to decelerate with a constant acceleration of $2\,\dfrac{\text{m}}{\text{s}^2}$ and simultaneously car B also decelerates with a constant acceleration of $4\,\dfrac{\text{m}}{\text{s}^2}$. What is the speed of car B at the moment it reaches car A, in meters per second?
(1) $2$ (2) $8$ (3) $4$ (4) $6$

iran-konkur 2023 Q50 Velocity-time or acceleration-time graph interpretation View

50. The equation of motion of an object with mass $500\,\text{g}$ moving along the $x$-axis is, in SI units, $\vec{F} = (6 - 3t)\hat{i}$. The net average force exerted on this object during the time interval $t_1 = 1\,\text{s}$ to $t_2 = 3\,\text{s}$, in newtons, is:
(1) $3\hat{i}$ (2) $-3\hat{i}$ (3) $6\hat{i}$ (4) $-6\hat{i}$
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iran-konkur 2024 Q44 Velocity-time or acceleration-time graph interpretation View

44-- The position--time graph of a particle moving along the $x$-axis with constant acceleration is shown below. What is the magnitude of the average speed of the particle in the first 7 seconds?
\begin{minipage}{0.45\textwidth} [Figure: position-time graph with x(m) axis showing value 24 at top, curve passing through origin, reaching a minimum near t=2, then rising to 24 at t=7; t(s) axis shows values 2 and 7] \end{minipage} \begin{minipage}{0.45\textwidth} (1) $\dfrac{25}{8}$
(2) $\dfrac{25}{7}$
(3) $\dfrac{23}{8}$
(4) $\dfrac{23}{7}$ \end{minipage}

iran-konkur 2024 Q46 Velocity-time or acceleration-time graph interpretation View

46. The figure below shows the acceleration–time graph of a moving object that at moment $t = 0\,\text{s}$ has velocity $\vec{V} = +\!\left(8\,\dfrac{\text{m}}{\text{s}}\right)\hat{i}$ and has been moving. What is the average velocity of the object in these 8 seconds (in meters per second)?
[Figure: acceleration-time graph with $a\,(\frac{\text{m}}{\text{s}^2})$ on vertical axis and $t\,(\text{s})$ on horizontal axis. The graph shows $a = +2$ from $t=0$ to $t=3$, then $a = -6$ from $t=3$ to $t=8$.]

[(1)] $12$
[(2)] $15$
[(3)] $\dfrac{43}{4}$
[(4)] $\dfrac{53}{6}$

iran-konkur 2024 Q47 Distance in successive equal time intervals View

47. An object at moment $t = 0\,\text{s}$ starts moving from rest with constant acceleration. The displacement of this object in the $n$-th second is how many times the displacement in the second $n$ equals the displacement in the second two?
$$\frac{5}{3} \quad (1) \qquad \frac{9}{4} \quad (2) \qquad \frac{3}{2} \quad (3) \qquad 2n \quad (4)$$

jee-main 2002 Q4 Penetration and deceleration to rest View

If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?
(1) 1 cm
(2) 2 cm
(3) 3 cm
(4) 4 cm

jee-main 2002 Q5 Braking and stopping distance View

Speeds of two identical cars are $u$ and $4u$ at the specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is
(1) $1 : 1$
(2) $1 : 4$
(3) $1 : 8$
(4) $1 : 16$

jee-main 2003 Q6 Acceleration then deceleration (two-phase motion) View

A body travels a distance $s$ in $t$ seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration $f$ and in the second part with constant retardation $r$. The value of $t$ is given by
(1) $\sqrt{2s\left(\frac{1}{f} + \frac{1}{r}\right)}$
(2) $2s\left(\frac{1}{f} + \frac{1}{r}\right)$
(3) $\frac{2s}{\frac{1}{f} + \frac{1}{r}}$
(4) $\sqrt{2s(f + r)}$

jee-main 2004 Q3 Free-fall and vertical drop View

A ball is released from the top of a tower of height $h$ metres. It takes $T$ seconds to reach the ground. What is the position of the ball in $\mathrm { T } / 3$ seconds?
(1) $\mathrm { h } / 9$ metres from the ground
(2) $7 \mathrm {~h} / 9$ metres from the ground
(3) $8 \mathrm {~h} / 9$ metres from the ground
(4) $17 \mathrm {~h} / 18$ metres from the ground.

jee-main 2004 Q4 Braking and stopping distance View

An automobile travelling with speed of $60 \mathrm {~km} / \mathrm { h }$, can brake to stop within a distance of 20 cm . If the car is going twice as fast, i.e $120 \mathrm {~km} / \mathrm { h }$, the stopping distance will be
(1) 20 m
(2) 40 m
(3) 60 m
(4) 80 m

jee-main 2005 Q4 Acceleration then deceleration (two-phase motion) View

A car starting from rest accelerates at the rate $f$ through a distance $S$, then continues at constant speed for time $t$ and then decelerates at the rate $f/2$ to come to rest. If the total distance traversed is 15 S, then
(1) $S = ft$
(2) $\mathrm{S} = 1/6\, \mathrm{ft}^2$
(3) $\mathrm{S} = 1/2\, \mathrm{ft}^2$
(4) None of these

jee-main 2005 Q5 Real-world SUVAT application problem View

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at $2 \mathrm{~m}/\mathrm{s}^2$. He reaches the ground with a speed of $3 \mathrm{~m}/\mathrm{s}$. At what height, did he bail out?
(1) 91 m
(2) 182 m
(3) 293 m
(4) 111 m

jee-main 2005 Q6 Two bodies meeting or catching up View

Two points $A$ and $B$ move from rest along a straight line with constant acceleration $f$ and $f'$ respectively. If $A$ takes $m$ sec. more than $B$ and describes '$n$' units more than $B$ in acquiring the same speed then
(1) $\left(f - f'\right)m^2 = ff'n$
(2) $\left(f + f'\right)m^2 = ff'n$
(3) $\frac{1}{2}\left(f + f'\right)m = ff'n^2$
(4) $\left(f' - f\right)n = \frac{1}{2}ff'm^2$

jee-main 2005 Q13 Acceleration of a Block Under Applied Force with Kinetic Friction View

A particle of mass 0.3 kg is subjected to a force $F = -kx$ with $k = 15 \mathrm{~N}/\mathrm{m}$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
(1) $3 \mathrm{~m}/\mathrm{s}^2$
(2) $15 \mathrm{~m}/\mathrm{s}^2$
(3) $5 \mathrm{~m}/\mathrm{s}^2$
(4) $10 \mathrm{~m}/\mathrm{s}^2$

jee-main 2005 Q14 Flat Curve with Friction (Unbanked Road) View

Consider a car moving on a straight road with a speed of $100 \mathrm{~m}/\mathrm{s}$. The distance at which car can be stopped is $[\mu_\mathrm{k} = 0.5]$
(1) 800 m
(2) 1000 m
(3) 100 m
(4) 400 m

jee-main 2005 Q16 Energy conservation with friction or dissipative forces View

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
(1) 3.0 cm
(2) 2.0 cm
(3) 1.5 cm
(4) 1.0 cm

jee-main 2008 Q2 Two bodies meeting or catching up View

A body is at rest at $x = 0$. At $t = 0$, it starts moving in the positive $x$-direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$ direction with a constant speed. The position of the first body is given by $\mathrm { x } _ { 1 } ( \mathrm { t } )$ after time ' t ' and that of the second body by $x _ { 2 } ( t )$ after the same time interval. Which of the following graphs correctly describes $\left( x _ { 1 } - x _ { 2 } \right)$ as a function of time ' $t$ '?
(1), (2), (3), (4) [see graphs in original]

jee-main 2010 Q4 Relative velocity and observed length/time View

Two fixed frictionless inclined plane making an angle $30 ^ { \circ }$ and $60 ^ { \circ }$ with the vertical are shown in the figure. Two block $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?
(1) $4.9 \mathrm {~ms} ^ { - 2 }$ in horizontal direction
(2) $9.8 \mathrm {~ms} ^ { - 2 }$ in vertical direction
(3) zero
(4) $4.9 \mathrm {~ms} ^ { - 2 }$ in vertical direction

jee-main 2012 Q2 Velocity at an intermediate point of a uniformly accelerating body View

A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity $u$ and the guard's room passes with velocity $v$. The middle wagon of the train passes the pole with a velocity.
(1) $\frac { u + v } { 2 }$
(2) $\frac { 1 } { 2 } \sqrt { u ^ { 2 } + v ^ { 2 } }$
(3) $\sqrt { u v }$
(4) $\sqrt { \left( \frac { u ^ { 2 } + v ^ { 2 } } { 2 } \right) }$

jee-main 2012 Q2 Find acceleration from position or velocity View

The distance travelled by a body moving along a line in time $t$ is proportional to $t^{3}$. The acceleration-time $(a, t)$ graph for the motion of the body will be
(1) [graph 1] (2) [graph 2] (3) [graph 3] (4) [graph 4]

jee-main 2015 Q4 Vertical projection (up or down) from a height View

From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of $48 \mathrm {~m} / \mathrm { s }$. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration $g = 32 \mathrm {~m} / \mathrm { s } ^ { 2 }$, is:
(1) 112
(2) 88
(3) 128
(4) 100

jee-main 2017 Q2 Two bodies meeting or catching up View

A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$ and the car has acceleration $4 \mathrm {~m} \mathrm {~s} ^ { - 2 }$. The car will catch up with the bus after time :
(1) $\sqrt { 120 } \mathrm {~s}$
(2) 15 s
(3) $\sqrt { 110 } \mathrm {~s}$
(4) $10 \sqrt { 2 } \mathrm {~s}$

jee-main 2019 Q2 Relative velocity and observed length/time View

A passenger train of length $60 m$ travels at a speed of $80 \mathrm {~km} / \mathrm { hr }$. Another freight train of length $120 m$ travels at a speed of $30 \mathrm {~km} / \mathrm { hr }$. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is:
(1) $\frac { 5 } { 2 }$
(2) $\frac { 3 } { 2 }$
(3) $\frac { 11 } { 5 }$
(4) $\frac { 25 } { 11 }$

jee-main 2019 Q2 Work-energy theorem: finding speed or kinetic energy from net work View

A bullet of mass 20 g has an initial speed of $1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, just before it starts penetrating a mud wall of thickness 20 cm . If the wall offers a mean resistance of $2.5 \times 10 ^ { - 2 } \mathrm {~N}$, the speed of the bullet after emerging from the other side of the wall is close to:
(1) $0.7 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(2) $0.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(3) $0.1 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
(4) $0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$

jee-main 2019 Q4 Velocity-time or acceleration-time graph interpretation View

A particle starts from the origin at time $t = 0$ and moves along the positive $x$-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time $t = 5s$?
(1) $10 m$
(2) $9 m$
(3) $6 m$
(4) $3 m$

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LFM Pure and Mechanics

Indices and Surds 96

Exponential Functions 197

Laws of Logarithms 242

Exponential Equations & Modelling 28

Arithmetic Sequences and Series 363

Geometric Sequences and Series 159

Differentiation from First Principles 45

Tangents, normals and gradients 140

Stationary points and optimisation 505

Applied differentiation 76

Indefinite & Definite Integrals 502

Areas Between Curves 71

Areas by integration 221

Volumes of Revolution 68

Numerical integration 49

Vectors Introduction & 2D 211

Vectors 3D & Lines 524

Travel graphs 14

SUVAT in 2D & Gravity 31

Constant acceleration (SUVAT) 78

Variable acceleration (1D) 55

Variable acceleration (vectors) 32

Forces, equilibrium and resultants 24

Newton's laws and connected particles 21

Pulley systems 6

Motion on a slope 6

Friction 8

Momentum and Collisions 34

Moments 28

Parametric curves and Cartesian conversion 9

Parametric differentiation 13

Parametric integration 6

Projectiles 49