Motion in a straight line practice · Mixed difficulty

From the top of a tower, a stone is thrown up and reaches the ground in time ${t_1} = 9\mathrm{s}.$. A second stone is thrown down with the same speed and reaches the ground in time ${t_2} = 4$ s. A third stone is released from rest and reaches the ground in time ${t_3}$, which is equal to

The velocity of a particle depends upon the time $\mathrm{t}$ according to the equation: $\mathrm{v}=\sqrt{\mathrm{a b}}+\mathrm{b t}+\frac{\mathrm{c}}{\mathrm{d+t}}$. The physical quantities which are represented by $\mathrm{a, b, c}$ and $\mathrm{d}$, are in the following order:

Can an object maintain uniform velocity when its acceleration is not zero?

A body travels a distance $s_1$ with velocity $v_1$ and distance $s_2$ with velocity $v_2$ in the same direction. Calculate the average velocity of the body:

A ball kicked vertically up attains a height of 19.6m and returns to the point of throw. If the ball is in air for four second, then the value of acceleration due to gravity is

The position vector of particle changes with time according to the relation $r(t) = 15{t^2}\hat i + (4 - 20{t^2})\hat j$. What is the magnitude of the acceleration (in $m{s^{ - \mathrm{2}}}$) at t =1 ?

A body thrown vertically upward with an initial velocity of 1.4 m/s returns in 2s. The total displacement of the ball is

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 f/2 to come to rest. If the total distance traversed is 15 S, then

Two trains take 3 sec to pass one another when going in the opposite direction but only 2.5 sec if the speed of the one is increased by $50 \%$. The time one would take to pass the other when going in the same direction at their original speed is:

Assertion: When a body is subjected to a uniform acceleration, it always move in a straight line.

Reason: Straight line motion is the natural tendency of the body.

STATEMENT-1 : For an observer looking out through the window of a fast moving train, the nearby objects appear to move in the opposite direction to the train, while the distant objects appear to be stationary.

STATEMENT-2 : If the observer and the object are moving at velocities $\vec{v}_1$ and $\vec{v}_2$ respectively with reference to a laboratory frame, the velocity of the object with respect to the observer is $\vec{v}_2-\vec{v}_1$.

Assertion: Kinematic equations are exact and are always correct.
Reason: The definitions of instantaneous velocity and acceleration are true only for motion in which the magnitude and direction of acceleration are constant during motion.

Assertion : A body can have acceleration even if its velocity is zero at a given instant of time.

Reason : A body is momentarily at rest when it reverses its direction of motion.

A body travels the first half of the total distance with velocity $v_1$ and the second half with velocity $v_2.$ Calculate the average velocity.

Assertion: The distance traversed, during equal intervals of time, by a body falling from rest are in ratio $1 : 3 : 5 : 7 \ldots$ [Galileo's law of odd numbers]
Reason: A particle in one-dimensional motion with zero speed may have non-zero velocity.

A particle is projected vertically from the ground takes time $t_1=1 \mathrm{~s}$ upto point ${A},\,\,t_2=3 \mathrm{~s}$ from point ${A}$ to $B$, and time $t_3$ $=4 \mathrm{~s}$ from point $B$ to highest point. Find the height of the middle point of $A$ and $B$ from the ground.

Assertion : A body is momentarily at rest when it reverses the direction.

Reason : A body cannot have acceleration if its velocity is zero at a given instant of time.

Statement-I: When a particle moves with constant velocity its average velocity, its instantaneous velocity and its speed are all equal in magnitude.
Statement-II: If the average velocity of a particle moving on a straight line is zero in a time interval, then it is possible that the instantaneous velocity is never zero in the interval

A stone is dropped into a well in which the level of water is $\mathrm{h}$ below the top of the well. If $\mathrm{v}$ is velocity of sound, the time $\mathrm{T}$ after which the splash is heard is given by

A ball P is dropped vertically and another ball Q is thrown horizontally with the same velocities from the same height and at the same time. If air resistance is neglected, then

Assertion (A) : Acceleration of a moving particle can change its direction without any change in direction of velocity.

Reason (R) : If the direction of change in velocity vector changes, the direction of acceleration vector also changes.

A drunkard is walking along a straight road. He takes five steps forward and three steps backward and so on. Each step is $1 \mathrm{~m}$ long and takes $1 \mathrm{~s}$. There is a pit on the road $11 \mathrm{~m}$ away from the starting point. The drunkard will fall into the pit after

The incorrect statement(s) from the following is/are

I. A body having zero velocity will not necessarily have zero acceleration

II. A body having zero velocity will necessarily have zero acceleration

III. A body having uniform speed can have only uniform acceleration

IV. A body having non-uniform velocity will have zero acceleration

A car covers a distance of $\mathrm{S}$ on a straight road in 3 hours and then returns to the initial point in four hours. Then, its average velocity is

A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity is

A car moving with constant acceleration crosses two points A and B with velocities 10 m/s and 20 m/s in its path. Find the velocity of the car midway between A and B (in m/s)

A point particle starting from rest has a velocity that increase linearly with time such that v=pt, where $p = 4\mathrm{m}{\mathrm{s}^{ - 2}}$. The distance covered in the first 2 s will be

Find value of a if distance between the points $(-9 \mathrm{~cm}, \mathrm{a} \mathrm{cm})$ and $(3 \mathrm{~cm}, 3 \mathrm{~cm}$ ) is $13 \mathrm{~cm}$.

The coordinates of a moving particle at any time $t$ are given by, $x=2 t^3$ and $y=3 t^3$. Acceleration of the particle is given by

An aeroplane files around a square field ABCD of each side 1000 km. Its speed along AB is $250\;km\;{h^{ - 1}}$, along DA $100\;km\;{h^{ - 1}}$. Its average speed (in $km\;{h^{ - 1}}$)) over the entire trip is