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)]