Motion in a straight line practice · Medium

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

If $v=(2 t+1) \mathrm{m} / \mathrm{sec}$ then average velocity from ${t}=0$ to $t=2\, \mathrm{sec}$ is

The correct statement from the following is

If initial velocity of a body is $\vec u = 2\hat i - 2\hat j + 3\hat k$ and is changed to $\vec v = 2\hat i - 4\hat j + 5\hat k$ in a time of 10sec. Its accelerated vector is

A bullet travelling with a velocity of $16 \mathrm{~m} / \mathrm{s}$ penetrates a tree trunk and comes to rest in $0.4 \mathrm{~m}$. Find the time taken during the retardation.

Assertion: A body dropped from a given height and another body projected horizontally from the same height strike the ground simultaneously.
Reason: Horizontal velocity has no effect in the vertical direction.

A particle moves with uniform velocity. Which of the following statements about the motion of the particle is true?

A ball is dropped from a building of height $45m$. Simultaneously another ball is thrown up with a speed $40\,m/s$. The rate of change of relative speed of the ball is

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10\;m{s^{ - 1}}\,to\,20\;m{s^{ - 1}}$ while passing through a distance 135 m in t second. The value of t is