Motion in a Straight Line · Physics · JEE Main

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...

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...

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...

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...

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 ...

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...

The relation between time '$$t$$' and distance '$$x$$' is $$t=\alpha x^2+\beta x$$, where $$\alpha$$ and $$\beta$$ are constants. The relation between...

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...

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...

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 $t=2 s$...

The distance travelled by an object in time $$t$$ is given by $$s=(2.5) t^{2}$$. The instantaneous speed of the object at $$\mathrm{t}=5 \mathrm{~s}$$...

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...

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...

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...

From the $$\mathrm{v}-t$$ graph shown, the ratio of distance to displacement in $$25 \mathrm{~s}$$ of motion is: ...

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...

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) ...

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 : ...

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{...

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...

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}...

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...

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 :-

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...

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...

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...

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...

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 $$...

If $$\mathrm{t}=\sqrt{x}+4$$, then $$\left(\frac{\mathrm{d} x}{\mathrm{~d} t}\right)_{\mathrm{t}=4}$$ is :

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...

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...

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...

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...

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...

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...

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...

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...

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 :...

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...

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...

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...

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 ...

The velocity $$-$$ displacement graph of a particle is shown in the figure.The acceleration $$-$$ displacement graph of the same particle is represent...

The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :

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 :

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...

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...

The velocity-displacement graph describing the motion of bicycle is shown in the figure.The acceleration-displacement graph of the bicycle's motion is...

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 ...

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...

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 ...

If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph?...

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...

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 ...

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...

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...

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...

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...

The position vector of a particle changes with time according to the relation $$\overrightarrow r (t) = 15{t^2}\widehat i + (4 - 20{t^2})\widehat j$$ ...

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...

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...

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...

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...

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...

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

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...

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 ...

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...

Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity ?

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

Two stones are thrown up simultaneously from the edge of a cliff $$240$$ $$m$$ high with initial speed of $$10$$ $$m/s$$ and $$40$$ $$m/s$$ respective...

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...

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...

Consider a rubber ball freely falling from a height $$h=4.9$$ $$m$$ onto a horizontal elastic plate. Assume that the duration of collision is negligi...

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...

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...

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...

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 ...

The relation between time t and distance x is t = ax2 + bx where a and b are constants. The acceleration is

A parachutist after bailing out falls $$50$$ $$m$$ without friction. When parachute opens, it decelerates at $$2\,\,m/{s^2}.$$ He reaches the ground ...

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 ...

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...

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...

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...

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 ...

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...

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...

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}$...

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 ...

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...

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...

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...

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...

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 ...

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...

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...

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...

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 ____________...

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...

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,...

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...

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...

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...

A particle is moving with constant acceleration 'a'. Following graph shows v2 versus x(displacement) plot. The acceleration of the particle is _______...

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 ...........

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...

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 =...

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...