A ball projected vertically upwards with a velocity ' $V$ ' passes through a point $P$ in its upward journey in a time of ' $x$ ' seconds. From there, the time in which the ball again passes through the same point $P$ is

Two smooth inclined planes $A$ and $B$ each of height 20 m have angles of inclination $30^{\circ}$ and $60^{\circ}$ respectively. If $t_1$ and $t_2$ are respectively the times taken by two blocks to reach the bottom of the planes $A$ and $B$ from the top, then $t_1-t_2=$ (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The displacement $(x)$ and time $(t)$ graph of a particle moving along a straight line is shown in the figure. The average velocity of the particle in the time of 10 s is

A body starts from rest with uniform acceleration and its velocity at a time of ' $n$ ' seconds is ' $v$ '. The total displacement of the body in the $n$th and $(n-1)$ th seconds of its motion is

A particle moving along a straight line covers the first half of the distance with a speed of $3 \mathrm{~ms}^{-1}$, the other half of the distance is covered in two equal time intervals with speeds of $4.5 \mathrm{~ms}^{-1}$ and $7.5 \mathrm{~ms}^{-1}$ respectively, then the average speed of particle during the motion is

If the distance travelled by a freely falling body in the last but one second of its motion is 5 m , then the last second is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The ratio of the displacements of a freely falling body during second and fifth seconds of its motion is

If a car travels $40 \%$ of the total distance with a speed $v_1$ and the remaining distance with a speed $v_2$, then average speed of the car is

A particle starts from rest and moves in a straight line. It travels a distance $2 L$ with uniform acceleration and then moves with a constant velocity a further distance of $L$. Finally, it comes to rest after moving a distance of $3 L$ under uniform retardation. Then, the ratio of average speed to the maximum speed $\left(\frac{v}{v_m}\right)$ of the particle is

The acceleration of a particle which moves along the positive $X$-axis varies with its position as shown in the figure. If the velocity of the particle is $0.8 \mathrm{~ms}^{-1}$ at $x=0$ , then its velocity at $x=1.4 \mathrm{~m}$ is $\left(\right.$ in $\left.\mathrm{ms}^{-1}\right)$

A student is at a distance 16 m from a bus when the bus begins to move with a constant acceleration of $$9 \mathrm{~m} \mathrm{~s}^{-2}$$. The minimum velocity with which the student should run. towards the bus so as the catch it is $$\alpha \sqrt{2} \mathrm{~ms}^{-1}$$. The value of $$\alpha$$ is

An object moving along $$X$$-axis with a uniform acceleration has velocity $$\mathbf{v}=\left(12 \mathrm{cms}^{-1}\right) \hat{\mathbf{i}}$$ at $$x=3 \mathrm{~cm}$$. After 2 s if it is at $$x=-5 \mathrm{~cm}$$, then its acceleration is

$$y=\left(P t^2-Q t^3\right) \mathrm{~m}$$ is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is

A car covers a distance at speed of $$60 \mathrm{~km} \mathrm{~h}^{-1}$$. It returns and comes back to the original point moving at a speed of $$v$$. If the average speed for the round trip is $$48 \mathrm{~kmh}^{-1}$$, then the magnitude of $$v$$ is

An object is moving with a uniformacceleration which is parallel to itsinstantaneous direction of motion. Thedisplacement-velocity graph of this object is

The displacement of a particle starting from rest at $$t=0$$ is given by $$s=9 t^2-2 t^3$$. The time in seconds at which the particle will attain zero velocity is

Two cars A and B are moving with a velocityof 30 km/h in the same direction. They areseparated by 10 km. The speed of another carC moving in the opposite direction, if it meetsthese two cars at an interval of eight minutesis

An object travelling at a speed of 36 km/hcomes to rest in a distance of 200 m after thebrakes were applied. The retardationproduced by the brakes is

A ball is projected upwards. Its accelerationat the highest point is

Which of the following decreases, in motionon a straight line, with constant retardation?