Motion in a Straight Line

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 :

[JEE Main 2024, 9 Apr (Shift 1)]

A block of mass \(1\) kg , moving along x with speed \({\mathrm{v}}_{\mathrm{i}}=10\mathrm{m}/\mathrm{s}\) enters a rough region ranging from \(\mathrm{x}=0.1\mathrm{m}\) to \(\mathrm{x}=1.9\mathrm{m}\). The retarding force acting on the block in this range is \({\mathrm{F}}_{\mathrm{r}}=-\mathrm{kxN}\), with \(\mathrm{k}=10\mathrm{N}/\mathrm{m}\). Then the final speed of the block as it crosses rough region is

[JEE Main 2025, 3 Apr (Shift 2)]

A bullet is fired into a fixed target looses one third of its velocity after travelling \(4 cm\). It penetrates further \(D \times 10^{-3} m\) before coming to rest. The value of \(D\) is :

[JEE Main 2024, 27 Jan (Shift 2)]

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 :

[JEE Main 2024, 9 Apr (Shift 1)]

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 :

[JEE Main 2024, 06 Apr (Shift 2)]

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 :

[JEE Main 2024, 06 Apr (Shift 2)]

Position of an ant ( \(S\) in metres) moving in \(Y-Z\) plane is given by \(S=2 t^2 \hat{j}+5 \hat{k}\) (where \(t\) is in second). The magnitude and direction of velocity of the ant at \(t=1 s\) will be :

[JEE Main 2024, 27 Jan (Shift 1)]

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 :

[JEE Main 2024, 9 Apr (Shift 1)]

The drift velocity of electrons for a conductor connected in an electrical circuit is V_d. The conductor is now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of the electrons will be

Two cars are travelling towards each other at speed of \(20 m s ^{-1}\) each. When the cars are \(300 m\) apart, both the drivers apply brakes and the cars retard at the rate of \(2 m s ^{-2}\). The distance between them when they come to rest is :

[JEE Main 2024, 09 Apr (Shift 2)]

Two cars are travelling towards each other at speed of \(20 m s ^{-1}\) each. When the cars are \(300 m\) apart, both the drivers apply brakes and the cars retard at the rate of \(2 m s ^{-2}\). The distance between them when they come to rest is :

[JEE Main 2024, 09 Apr (Shift 2)]

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 :

[JEE Main 2024, 6 Apr (Shift 2)]

A clock has 75 cm , 60 cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel x distance more than the tip of minute hand. The value of x in meter is nearly (Take \(\pi =3.14\) ) :

The position of a particle varies with time as \(\vec{r}=\left(5 t^2 \hat{\imath}-5 t \hat{\jmath}\right) \mathrm{m}\). The magnitude and direction of velocity at \(t=\frac{1}{2} \mathrm{~s}\) is

A particle moves along the x-axis and has its displacement x varying with time t according to the equation \(\mathrm{x}={\mathrm{c}}_{0}\left({\mathrm{t}}^{2}-2\right)+\mathrm{c}(\mathrm{t}-2{)}^{2}\) where \({\mathrm{c}}_{0}\) and c are constants of appropriate dimensions. Then, which of the following statements is correct?

[JEE Main 2025, 3 Apr (Shift 2)]

Position of an ant ( \(S\) in metres) moving in \(Y-Z\) plane is given by \(S=2 t^2 \hat{j}+5 \hat{k}\) (where \(t\) is in second). The magnitude and direction of velocity of the ant at \(t=1 s\) will be :

A satellite is nine times closer to earth compared to moon. Time period of moon is 27 days then period of satellite is

(Shift - II Memory Based)

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 :

[JEE Main 2024, 9 Apr (Shift 1)]

Position of an ant ( \(S\) in metres) moving in \(Y-Z\) plane is given by \(S=2 t^2 \hat{j}+5 \hat{k}\) (where \(t\) is in second). The magnitude and direction of velocity of the ant at \(t=1 s\) will be :

A bullet is fired into a fixed target loses one third of its velocity after travelling \(4 \ cm\). It penetrates further \(D \times 10^{-3} \ m\) before coming to rest. The value of \(D \) is : (assuming constant retardation)

A satellite is nine times closer to earth compared to moon. Time period of moon is 27 days then period of satellite is

(Shift - II Memory Based)

Two cars A and B are moving in the same direction along a straight line with speeds 100 km/h and 80 km/h, respectively such that car A is moving ahead of car B. A person in car B throws a stone with a speed v so that it hits the car A with a speed of 5 m/s. The value of v is _____ km/h.

[JEE Main 2026, 4 Apr (Shift 2)]

A gas balloon is going up with a constant velocity of 10 m / s. When this balloon reached a height of 75 m , a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is m . ( Take \(\left.g=10m/{s}^{2}\right)\)

[JEE Main 2026, 8 Apr (Shift 2)]

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 km/h and 72 km/h, respectively. If train ' A ' takes 35 s less time than train ' B ' to cross the tunnel then, length ' L' of tunnel is (Given L=60 l )

[JEE Main 2023, 13 Apr (Shift 1)]

A balloon is rising vertically up with a velocity of \(29 \mathrm{~ms}^{-1}\). A stone is dropped from it and it reaches the ground in 10 seconds. The height of the balloon when the stone was dropped from it, was \(\left(g=9.8 \mathrm{~ms}^{-2}\right)\)

A vehicle travels \(4 km\) with speed of \(3 km / h\) and another \(4 km\) with speed of \(5 km / h\), then its average speed is:

[JEE Main 2023, 30 Jan (Shift 2)]

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 \(75 m\) from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of \(g\) as \(\left.10 m / s ^2\right)\)

[JEE Main 2021, 25 Jul (Shift 2)]

The position vector of a particle related to time t is given by \(\vec{r}=\left(10 t \hat{i}+15 t^2 \hat{j}+7 \hat{k}\right) \mathrm{m}\) The direction of net force experienced by the particle is :

[JEE Main 2023, 15 Apr (Shift 1)]

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 drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor

[JEE Main 2021, 27 Aug (Shift 2)]

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 drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor

[JEE Main 2021, 27 Aug (Shift 2)]

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 person is \(v\), then the relation between \(v, v_1\) and \(v_2\) will be:

[JEE Main 2023, 10 Apr (Shift 2)]

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 drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor

The velocity of a particle is \( v=v_{0}+g t+f t^{2} \). If its position is \( x=0 \) at \( t=0 \), then its displacement after unit time ( \( t= \) 1) is

The numerical ratio of displacement to the distance covered is always:

[JEE Main 2023, 25 Jan (Shift 2)]

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 km/h and 72 km/h, respectively. If train ' A ' takes 35 s less time than train ' B ' to cross the tunnel then, length ' L' of tunnel is (Given L=60 l )

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 the car 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 the car is:

[JEE Main 2023, 25th June (Shift 1)]

Given below are two statements:
Statement-I: Area of the velocity-time graph gives the distance travelled by the body in a given time.
Statement-II: Area under acceleration- time graph is equal to the change in velocity- in the given time.

In the light of given statements, choose the correct answer from the options given below.

[JEE Main 2023, 8 Apr (Shift 2)]

The distance travelled by an object in time \(t\) is given by \(s=(2.5) t^2\). The instantaneous speed of the object at (t = 5 s) will be:

[JEE Main 2023, 13 Apr (Shift 2)]

A particle starts with an initial velocity of \(10.0 ms ^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0 ms ^{-2}\). The time taken by the particle to reach the velocity of \(60.0 ms ^{-1}\) is

[JEE Main 2023, 6 Apr (Shift 1)]

A bullet from a gun is fired on a rectangular wooden block with velocity \(u\). When bullet travels \(24 \mathrm{~cm}\) through the block along its length horizontally, velocity of bullet becomes \(\frac{u}{3}\). Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

[NEET 2023]

The distance travelled by a particle is related to time t as x = 4t². The velocity of the particle at t = 5s is

[JEE Main 2023, 25 Jan (Shift 2)]

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 with which middle point of the train passes the signal post is:

[JEE Main 2021, 25 Feb (Shift 1)]

Train A and train B are running on parallel tracks in opposite directions with speeds of 36km/hour and 72 km/hour, respectively, A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km / hour. Speed (in \(m{s}^{-1}\)) of this person as observed from train B will be close to: (take the distance between the tracks as negligible)

[JEE Main 2020, 2 Sep (Shift 1)]