Motion in a straight line practice · Medium

A train $175 \mathrm{~m}$ long crosses a bridge which is $225 \mathrm{~m}$ long in 80 seconds. What is the speed of the train?

The motion of a particle moving along $y$-axis is represented as $y=3(t-2)+5(t-2)^2.$ Identify the correct statement.

A graph is drawn between velocity and time for the motion of a particle. The area under the curve between the time intervals ${t_1}\,and\,\,{t_2}$ gives

Assertion (A) : A body is dropped from height $h$ and another body is thrown vertically upwards with a speed $\sqrt{g h}$. They meet at height $h / 2$.

Reason (R) : The time taken by both the blocks in reaching the height $h / 2$ is same.

The displacement of a particle starting from rest (at t=0) is given by $s = 6{t^2} - {t^3}.$. The time in seconds at which the particle will attain zero velocity again, is

A body starts from rest and travels a distance S with uniform acceleration, then moves uniformly a distance 2 S uniformly, and finally comes to gest after moving further 5 S under uniform retardation. The ratio of average velocity to maximum velocity is

Two trains $121 \mathrm{~m}$ and $99 \mathrm{~m}$ in lengths are running in opposite directions with velocities $40 \mathrm{~km} / \mathrm{h}$ and $32 \mathrm{~km} / \mathrm{h}$. In what time they will completely cross each other?

A person travels along a straight road for the first half time with a velocity $v_1$ and the second half time with a velocity $v_2$. Then the mean velocity $\bar{v}$ is given by

A bus starts from rest and moves along a straight road with constant acceleration $f$ until its speed is $v$. The bus then continues with constant speed $v$. When the bus starts, a car is at a distance $b$ behind the bus and is moving with constant speed $u$ in same direction as that of bus. Find the distance between the car and the bus at time $t$ after the bus started.

(Given $0 < t < \frac{v}{f}$ and $u^2 < 2 f b$).

A body is moving with uniform velocity of $8 \mathrm{~ms}^{-1}$. When the body just crossed another body, the second one starts and moves with uniform acceleration of $4 \mathrm{~ms}^{-2}$. The time after which two bodies meet, will be

A train is moving with a velocity of $30 \mathrm{~ms}^{-1}$. When brakes are applied, it is found that the velocity reduced to $10 \mathrm{~ms}^{-1}$ in $240 \mathrm{~m}$. When the velocity of the train is zero, the distance travelled is

A train started from rest from a station and accelerated at $2\,m{s^{ - 2}}$ for 10sec. Then it travels at constant speed for 30 sec and there after it decelerated at $4\,m{s^{ - 2}}$ until it stopped at the next station. The distance between two stations is

A ball which is at rest is dropped from a height h metre. As it bounces off the floor its speed is 80% of what it was just before touching the ground. The ball then rise to nearly a height

Two stones of equal masses are dropped from a rooftop of height h one after another. Their separation distance against time will

Assertion(A): Average velocity can't be zero in case of uniform acceleration.

Reason (R): For average velocity to be zero, a non zero velocity should not remain constant.

Assertion: In one-dimensional motion of an object, path length comes out to be equal to displacement.
Reason: Direction of object is changed two times.

Assertion: An object may have varying speed without having varying velocity.
Reason: If the velocity is zero at an instant, the acceleration may not be zero at that instant.

Assertion: For a moving object the instantaneous velocity is calculated by the limiting value of its average velocity as the time interval approaches to zero.
Reason: The direction of the average velocity is same as the direction of displacement.

Assertion: For an object in uniform motion, the position-time graph is a straight line inclined to the time-axis.

Reason: In a uniform motion, the acceleration is zero.

A particle starts from the origin of coordinates at time t=0 and moves in the x-y plane with a constant acceleration&nbsp;$\alpha$ in the y-diretion. Its equation of motion is $y = \mathrm{\beta }{x^2}$. Its velocity component in the x-direction is

A particle moves in a straight line, so that after $t$ second the distance $x$ from a fixed point $O$ on the line is given by $x=(t-2)^2(t-5)$. Then

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three seconds of its motion. The stone remains in the air for

Assertion: An object can have an acceleration even if its speed is zero at a given instant.

Reason: An object was momentarily at rest when reversing its direction of travel.

A ball is thrown vertically upwards with a velocity of $25\;m{s^{ - 1}}$ from the top of a tower of height 30 m. How long will it travel before it hits ground

A ball is dropped form the building of height $45\,\,m$ simultaneously another ball is thrown up with a speed $40\,\,m/s$. The rate of change of relative speed of the ball is $\left[ {m{s^{ - 1}}} \right]$

A ball is released from a height $\mathrm{h}$ above the ground. It takes a time $\mathrm{T}$ to reach the ground. Where is the ball at the time $\mathrm{T} / 2$

A stone dropped from a balloon which is at a height h, reaches the ground after t second. From the same balloon, if two stones are thrown, one upwards and the other downwards, with the same velocity u and they reach the ground after ${t_1}$ and ${t_2}$ second respectively, then

For a $1-D$ motion, relation between position $x$ and time $t$ is $t=\alpha x^2+\beta x$. Find the relation between velocity $v$ and acceleration $a$.

A body is fired vertically upward. At half the maximum height, the velocity of the body is 10m/s. The maximum height raised by the body is

The velocity $v$ of a particle as a function of its position $(x)$ is expressed as $v=\sqrt{c_1-c_2 x}$, where $c_1$ and $c_2$ are positive constants. The acceleration of the particle is