Motion in a Straight Line

If the displacement ( $s$ in metre) of a moving particle in terms of time $(t$ in second $) s=t^3-6 t^2+18 t+9$, then the minimum velocity attained by the particle is

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...

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

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 $=10 \mathrm{~ms}^{-2}$ )

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 \math...

If a stone thrown vertically upwards from a bridge with an initial velocity of $5 \mathrm{~ms}^{-1}$, strikes the water below the bridge in a time of 3 s , then the height of the bridge above the water surface is
(Acceleration due to gravit...

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 diving board is at at height of $h$ from the water surface. A swimmer standing on this board thrown a stone vertically upward with a velocity $16 \mathrm{~ms}^{-1}$. It reaches the water surface in a time of 5 s . In the next 0.2 s the di...

A person walks up a stalled escalator in 90 s. When standing on the same moving escalator, he reached in 60s. The time it would take him to walk up the moving escalator will be

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 $3 L$ un...

An object projected upwards from the foot of a tower. The object crosses the top of the tower twice with an interval of 8 s and the object reaches foot after 16 s . The height of the tower is $\left(g=10 \mathrm{~ms}^{-2}\right)$

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...

The velocity of a particle is given by the equation $v(x)=3 x^2-4 x$, where $x$ is the distance covered by the particle. The expression for its acceleration is

A body starting from rest moving with an acceleration of $\frac{5}{4} \mathrm{~ms}^{-2}$. The distance travelled by the body in the third second is

The relation between time $t$ and displacement $x$ is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. If $v$ is the velocity, the retardation is

A car travelling at 80 kmph can be stopped at a distance of 60 m by applying brakes. If the same car travels at 160 kmph and the same braking force is applied, the stopping distance is

The time of flight of a vertically projected stone is 8 s . the position of the stone after 6 s from the ground is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A truck moving with a constant velocity $12 \mathrm{~ms}^{-1}$ crosses a car moving from rest with uniform acceleration $2 \mathrm{~ms}^{-2}$. The distance the car has to travel from the starting point to cross the truck again is

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 $$\alph...

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 o...

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

Two cars A and B are moving with a velocity
of 30 km/h in the same direction. They are
separated by 10 km. The speed of another car
C moving in the opposite direction, if it meets
these two cars at an interval of eight minutes
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

An object is moving with a uniform
acceleration which is parallel to its
instantaneous direction of motion. The
displacement-velocity graph of this object is

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

A ball is projected upwards. Its acceleration
at the highest point is

An object travelling at a speed of 36 km/h
comes to rest in a distance of 200 m after the
brakes were applied. The retardation
produced by the brakes is