# Motion in a Straight Line · Physics · JEE Main

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JEE Main 2024 (Online) 9th April Evening Shift
Two cars are travelling towards each other at speed of $$20 \mathrm{~m} \mathrm{~s}^{-1}$$ each. When the cars are $$300 \mathrm{~m}$$ apart, both the...
JEE Main 2024 (Online) 9th April Morning Shift
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 i...
JEE Main 2024 (Online) 6th April Evening Shift
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 downward...
JEE Main 2024 (Online) 6th April Morning Shift
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...
JEE Main 2024 (Online) 4th April Morning Shift
A body travels $$102.5 \mathrm{~m}$$ in $$\mathrm{n}^{\text {th }}$$ second and $$115.0 \mathrm{~m}$$ in $$(\mathrm{n}+2)^{\text {th }}$$ second. The ...
JEE Main 2024 (Online) 1st February Evening Shift
Train A is moving along two parallel rail tracks towards north with speed $$72 \mathrm{~km} / \mathrm{h}$$ and train B is moving towards south with sp...
JEE Main 2024 (Online) 31st January Morning Shift
The relation between time '$$t$$' and distance '$$x$$' is $$t=\alpha x^2+\beta x$$, where $$\alpha$$ and $$\beta$$ are constants. The relation between...
JEE Main 2024 (Online) 29th January Evening Shift
A particle is moving in a straight line. The variation of position '$$x$$' as a function of time '$$t$$' is given as $$x=\left(t^3-6 t^2+20 t+15\right... JEE Main 2024 (Online) 29th January Morning Shift A body starts moving from rest with constant acceleration covers displacement$$S_1$$in first$$(p-1)$$seconds and$$\mathrm{S}_2$$in first$$p$$s... JEE Main 2023 (Online) 15th April Morning Shift The position of a particle related to time is given by x=\left(5 t^{2}-4 t+5\right) \mathrm{m}. The magnitude of velocity of the particle at t=2 s... JEE Main 2023 (Online) 13th April Evening Shift The distance travelled by an object in time$$t$$is given by$$s=(2.5) t^{2}$$. The instantaneous speed of the object at$$\mathrm{t}=5 \mathrm{~s}$$... JEE Main 2023 (Online) 13th April Evening Shift A passenger sitting in a train A moving at$$90 \mathrm{~km} / \mathrm{h}$$observes another train$$\mathrm{B}$$moving in the opposite direction for... JEE Main 2023 (Online) 13th April Morning Shift Two trains 'A' and 'B' of length '$$l$$' and '$$4 l$$' are travelling into a tunnel of length '$$\mathrm{L}$$' in parallel tracks from opposite direct... JEE Main 2023 (Online) 12th April Morning Shift A ball is thrown vertically upward with an initial velocity of$$150 \mathrm{~m} / \mathrm{s}$$. The ratio of velocity after$$3 \mathrm{~s}$$and$$5...
JEE Main 2023 (Online) 11th April Morning Shift
From the $$\mathrm{v}-t$$ graph shown, the ratio of distance to displacement in $$25 \mathrm{~s}$$ of motion is: ...
JEE Main 2023 (Online) 10th April Evening Shift
A person travels $$x$$ distance with velocity $$v_{1}$$ and then $$x$$ distance with velocity $$v_{2}$$ in the same direction. The average velocity of...
JEE Main 2023 (Online) 10th April Morning Shift
The position-time graphs for two students A and B returning from the school to their homes are shown in figure. (A) A lives closer to the school (B) ...
JEE Main 2023 (Online) 8th April Evening Shift
Given below are two statements Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time. Statement II : ...
JEE Main 2023 (Online) 6th April Evening Shift
A particle starts with an initial velocity of $$10.0 \mathrm{~ms}^{-1}$$ along $$x$$-direction and accelerates uniformly at the rate of $$2.0 \mathrm{... JEE Main 2023 (Online) 1st February Morning Shift An object moves with speed$$v_1,v_2$$and$$v_3$$along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, the... JEE Main 2023 (Online) 30th January Evening Shift A vehicle travels 4 \mathrm{~km} with speed of 3 \mathrm{~km} / \mathrm{h} and another 4 \mathrm{~km} with speed of 5 \mathrm{~km} / \mathrm{h}... JEE Main 2023 (Online) 30th January Morning Shift Match Column-I with Column-II : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font... JEE Main 2023 (Online) 25th January Evening Shift The distance travelled by a particle is related to time t as$$x=4\mathrm{t}^2$$. The velocity of the particle at t=5s is :- JEE Main 2023 (Online) 25th January Morning Shift A car travels a distance of '$$x$$' with speed$$v_1$$and then same distance '$$x$$' with speed$$v_2$$in the same direction. The average speed of t... JEE Main 2023 (Online) 24th January Evening Shift The velocity time graph of a body moving in a straight line is shown in the figure. The ratio of displacement to distance travelled by the body in ti... JEE Main 2022 (Online) 29th July Evening Shift A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball... JEE Main 2022 (Online) 29th July Evening Shift A ball is released from a height h. If$$t_{1}$$and$$t_{2}$$be the time required to complete first half and second half of the distance respectivel... JEE Main 2022 (Online) 29th July Morning Shift A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height$$...
JEE Main 2022 (Online) 29th July Morning Shift
If $$\mathrm{t}=\sqrt{x}+4$$, then $$\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$$ is :
JEE Main 2022 (Online) 28th July Morning Shift
A NCC parade is going at a uniform speed of $$9 \mathrm{~km} / \mathrm{h}$$ under a mango tree on which a monkey is sitting at a height of $$19.6 \mat... JEE Main 2022 (Online) 27th July Evening Shift The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during i... JEE Main 2022 (Online) 27th July Morning Shift A bullet is shot vertically downwards with an initial velocity of$$100 \mathrm{~m} / \mathrm{s}$$from a certain height. Within 10 s, the bullet reac... JEE Main 2022 (Online) 29th June Evening Shift A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t s, the distance travelled by t... JEE Main 2022 (Online) 29th June Morning Shift Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an init... JEE Main 2022 (Online) 25th June Evening Shift Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by$${X_P}(t) = \alpha t + \beta...
JEE Main 2021 (Online) 27th August Evening Shift
Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first...
JEE Main 2021 (Online) 27th July Morning Shift
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 $${h \over... JEE Main 2021 (Online) 25th July Evening Shift The relation between time t and distance x for a moving body is given as t = mx2 + nx, where m and n are constants. The retardation of the motion is :... JEE Main 2021 (Online) 25th July Evening Shift A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m f... JEE Main 2021 (Online) 25th July Evening Shift The instantaneous velocity of a particle moving in a straight line is given as$$V = \alpha t + \beta {t^2}$$, where$$\alpha$$and$$\beta$$are cons... JEE Main 2021 (Online) 25th July Morning Shift Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at 4th second after its fall to the next dropl... JEE Main 2021 (Online) 20th July Evening Shift A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a ... JEE Main 2021 (Online) 18th March Evening Shift The velocity$$-$$displacement graph of a particle is shown in the figure.The acceleration$$-$$displacement graph of the same particle is represent... JEE Main 2021 (Online) 18th March Morning Shift The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by : JEE Main 2021 (Online) 17th March Evening Shift The velocity of a particle is v = v0 + gt + Ft2. Its position is x = 0 at t = 0; then its displacement after time (t = 1) is : JEE Main 2021 (Online) 17th March Evening Shift A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to$${{81} \over {100}}$$of the height thro... JEE Main 2021 (Online) 17th March Morning Shift A car accelerates from rest at a constant rate$$\alpha$$for some time after which it decelerates at a constant rate$$\beta$$to come to rest. If th... JEE Main 2021 (Online) 16th March Morning Shift The velocity-displacement graph describing the motion of bicycle is shown in the figure.The acceleration-displacement graph of the bicycle's motion is... JEE Main 2021 (Online) 26th February Evening Shift A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value ... JEE Main 2021 (Online) 25th February Evening Shift A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top... JEE Main 2021 (Online) 25th February Morning Shift An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity ... JEE Main 2021 (Online) 24th February Morning Shift If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?... JEE Main 2020 (Online) 5th September Evening Slot The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance co... JEE Main 2020 (Online) 5th September Morning Slot A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is ... JEE Main 2020 (Online) 4th September Morning Slot A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height$${h \over 2}$$. The velocity vers... JEE Main 2020 (Online) 2nd September Morning Slot Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walk... JEE Main 2019 (Online) 12th April Evening Slot A particle is moving with speed v = b$$\sqrt x $$along positive x-axis. Calculate the speed of the particle at time t =$$\tau $$(assume that the par... JEE Main 2019 (Online) 9th April Evening Slot The position of a particle as a function of time t, is given byx(t) = at + bt2 – ct3 where a, b and c are constants. When the particle attains zero ac... JEE Main 2019 (Online) 9th April Evening Slot The position vector of a particle changes with time according to the relation$$\overrightarrow r (t) = 15{t^2}\widehat i + (4 - 20{t^2})\widehat j$$... JEE Main 2019 (Online) 8th April Evening Slot A particle starts from origin O from rest and moves with a uniform acceleration along the positive x-axis. Identify all figures that correctly represe... JEE Main 2019 (Online) 12th January Morning Slot A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of ti... JEE Main 2019 (Online) 11th January Evening Slot A particle moves from the point$$\left( {2.0\widehat i + 4.0\widehat j} \right)$$m, at t = 0, with an initial velocity$$\left( {5.0\widehat i + 4.0...
JEE Main 2019 (Online) 10th January Evening Slot
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. Wh...
JEE Main 2019 (Online) 9th January Evening Slot
In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '$$\upsilon$$' more than t...
JEE Main 2018 (Offline)
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.
JEE Main 2018 (Online) 15th April Morning Slot
An automobile, travelling at $$40\,$$ km/h, can be stopped at a distance of $$40\,$$ m by applying brakes. If the same automobile is travelling at $$8... JEE Main 2018 (Online) 15th April Morning Slot The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter ... JEE Main 2017 (Online) 9th April Morning Slot A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bu... JEE Main 2017 (Online) 8th April Morning Slot Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ? JEE Main 2017 (Offline) A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time? JEE Main 2015 (Offline) Two stones are thrown up simultaneously from the edge of a cliff$$240m$$high with initial speed of$$10m/s$$and$$40m/s$$respective... JEE Main 2014 (Offline) From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that t... AIEEE 2011 An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by :$${{dv} \over {dt}} = - 2.5\sqrt v $$where v is the instantaneous sp... AIEEE 2009 Consider a rubber ball freely falling from a height$$h=4.9m$$onto a horizontal elastic plate. Assume that the duration of collision is negligi... AIEEE 2008 A body is at rest at$$x=0.$$At$$t=0,$$it starts moving in the positive$$x$$-direction with a constant acceleration. At the same instant another b... AIEEE 2007 The velocity of a particle is v = v0 + gt + ft2. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is... AIEEE 2006 A particle located at x = 0 at time t = 0, starts moving along the positive x-direction with a velocity 'v' that varies as$$v = \alpha \sqrt x $$. Th... AIEEE 2005 A car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate ... AIEEE 2005 The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is AIEEE 2005 A parachutist after bailing out falls$$50m$$without friction. When parachute opens, it decelerates at$$2\,\,m/{s^2}.$$He reaches the ground ... AIEEE 2004 A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in$${T \over ...
AIEEE 2004
An automobile travelling with speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e 120 km/h, the stop...
AIEEE 2003
A car, moving with a speed of 50 km/hr, can be stopped by brakes after at least 6 m. If the same car is moving at a speed of 100 km/hr, the minimum st...
AIEEE 2003
The co-ordinates of a moving particle at any time 't' are given by x = $$\alpha$$t3 and y = βt3. The speed to the particle at time 't' is given by...
AIEEE 2002
From a building two balls A and B are thrown such that A is thrown upwards and B downwards ( both vertically with the same speed ). If vA and vB are ...
AIEEE 2002
Speeds of two identical cars are $$u$$ and $$4$$$$u$$ at the specific instant. The ratio of the respective distances in which the two cars are stopp...

## Numerical

JEE Main 2024 (Online) 6th April Evening Shift
A particle moves in a straight line so that its displacement $$x$$ at any time $$t$$ is given by $$x^2=1+t^2$$. Its acceleration at any time $$\mathrm... JEE Main 2024 (Online) 5th April Morning Shift A body moves on a frictionless plane starting from rest. If$$\mathrm{S_n}$$is distance moved between$$\mathrm{t=n-1}$$and$$\mathrm{t}=\mathrm{n}$... JEE Main 2024 (Online) 4th April Evening Shift A bus moving along a straight highway with speed of $$72 \mathrm{~km} / \mathrm{h}$$ is brought to halt within $$4 s$$ after applying the brakes. The ... JEE Main 2024 (Online) 1st February Evening Shift A particle initially at rest starts moving from reference point$x=0$along$x$-axis, with velocity$v$that varies as$v=4 \sqrt{x} \mathrm{~m} / \ma...
JEE Main 2024 (Online) 1st February Morning Shift
A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origi...
JEE Main 2024 (Online) 30th January Morning Shift
The displacement and the increase in the velocity of a moving particle in the time interval of $$t$$ to $$(t+1) \mathrm{s}$$ are $$125 \mathrm{~m}$$ a...
JEE Main 2024 (Online) 27th January Evening Shift
A body falling under gravity covers two points $$A$$ and $$B$$ separated by $$80 \mathrm{~m}$$ in $$2 \mathrm{~s}$$. The distance of upper point A fro...
JEE Main 2023 (Online) 1st February Evening Shift
For a train engine moving with speed of $$20 \mathrm{~ms}^{-1}$$, the driver must apply brakes at a distance of 500 $$\mathrm{m}$$ before the station ...
JEE Main 2023 (Online) 30th January Morning Shift
A horse rider covers half the distance with $$5 \mathrm{~m} / \mathrm{s}$$ speed. The remaining part of the distance was travelled with speed $$10 \ma... JEE Main 2023 (Online) 29th January Morning Shift A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The ave... JEE Main 2022 (Online) 28th July Evening Shift A ball is thrown vertically upwards with a velocity of$$19.6 \mathrm{~ms}^{-1}$$from the top of a tower. The ball strikes the ground after$$6 \math...
JEE Main 2022 (Online) 25th July Evening Shift
A particle is moving in a straight line such that its velocity is increasing at 5 ms$$-$$1 per meter. The acceleration of the particle is ____________...
JEE Main 2022 (Online) 25th July Morning Shift
A car is moving with speed of $$150 \mathrm{~km} / \mathrm{h}$$ and after applying the break it will move $$27 \mathrm{~m}$$ before it stops. If the s...
JEE Main 2022 (Online) 28th June Evening Shift
A car covers AB distance with first one-third at velocity v1 ms$$-$$1, second one-third at v2 ms$$-$$1 and last one-third at v3 ms$$-$$1. If v3 = 3v1,...
JEE Main 2022 (Online) 26th June Evening Shift
A ball is projected vertically upward with an initial velocity of 50 ms$$-$$1 at t = 0s. At t = 2s, another ball is projected vertically upward with s...
JEE Main 2022 (Online) 26th June Morning Shift
A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleratio...
JEE Main 2022 (Online) 24th June Morning Shift
From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same po...
JEE Main 2021 (Online) 31st August Evening Shift
A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The acceleration of the particle is _______...
JEE Main 2021 (Online) 27th August Morning Shift
If the velocity of a body related to displacement x is given by $$\upsilon = \sqrt {5000 + 24x}$$ m/s, then the acceleration of the body is ...........
JEE Main 2021 (Online) 26th August Morning Shift
Two spherical balls having equal masses with radius of 5 cm each are thrown upwards along the same vertical direction at an interval of 3s with the sa...
JEE Main 2020 (Online) 4th September Evening Slot
The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t =...
JEE Main 2020 (Online) 9th January Morning Slot
The distance x covered by a particle in one dimensional motion varies with time t as x2 = at2 + 2bt + c. If the acceleration of the particle depends o...
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