Motion in a straight line practice · Mixed difficulty

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

The acceleration of a particle increasing linearly with time t is bt. The particle starts from the origin with an initial velocity ${v_0}$. The distance travelled by the particle in time t will be

The ratio of the distance covered to the displacement of a particle moved along a semi-circle of radius $r$ is:

Which of the following is a one dimensional motion?

A particle comes round a circle of radius 1 m once. The time taken by it is 10 sec. The average velocity of motion is

Assertion: A lift is ascending with decreasing speed means acceleration of lift is downwards.
Reason: A body always moves in the direction of its acceleration.

An engine of a train moving with uniform acceleration passes the signal-post with velocity $u$ and the last compartment with velocity $v$. The velocity with which middle point of the train passes the signal post is

A ball is projected upwards from a height h above the surface of the earth with velocity v. The time at which the ball strikes the ground is

The ratio of distances traversed in successive intervals of time when a body falls freely under gravity from certain height is

Assertion: Doubling the initial velocity, the stopping distance of moving object increases by a factor of 4 (for the same deceleration).
Reason: Stopping distance is proportional to the square of the initial velocity.

Which of the following statement/s is/are correct?

Statement I: Only single value of distance is possible between two fixed points.

Statement II: Infinite values of displacements are possible between two fixed points.

A body start from rest and moves with constant acceleration. The ratio of distance covered by the body in $n\,{\text{th}}$ second to that covered in $n$ second is

A ball of mass $m$ and another ball of mass $2 m$ are dropped from equal heights. If the time taken by the balls to reach the ground are $t_1$ and $t_2$ respectively, then (neglect air drag)

From the top of a tower of height 50m, a ball is thrown vertically upwards with a certain velocity. It hits the ground 10 s after it is thrown up. How much time does it take to cover a distance AB where A and B are two points 20m and 40m below the edge of the tower? ($\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$)

A particle covers 4m, 5m, 6m, and 7m, in 3rd, 4th, 5th and 6th second respectively. The particle starts

The position of a particle moving along $x$-axis varies with time $t$ as $4 x+t^2=4$. At what position, the particle is at rest?

A particle moves in a straight line so that its displacement x metre at time t second is given by
$t = \sqrt {{x^2} - 1}$ Its acceleration in $\mathrm{m}{\mathrm{s}^{ - 2}}\mathrm{\;}$ at time t second is

A body is projected with a velocity 60 m/s vertically upwards the distance travelled in last second of its motion $[g = 10\,\,m\mathrm{/}{s^2}]$

The motion of a particle along a straight line is described by the equation: $x=8+12 t-t^3$, where ${x}$ is in meter and ${t}$ in second.

(i) the initial velocity of particle is $12 \mathrm{~m} / \mathrm{s}$

(ii) the retardation of particle when velocity is zero is $12 \mathrm{~m} / \mathrm{s}^2$

(iii) when acceleration is zero, displacement is $8 \mathrm{~m}$

(iv) the maximum velocity of particle is $12 \mathrm{~m} / \mathrm{s}$

Assertion: The magnitude of average velocity of an object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
Reason: Path length (distance) is either equal to or greater than the magnitude of displacement.

A particle starts from rest and moving with constant acceleration. Let ${S}_{{n}}$ and ${S}_{{n}+1}$ be the distance travelled by the particle in the time intervals ${t}={n}-1$ to ${t}={n}$ and ${t}={n}$ to ${t}={n}+1$ respectively. The ratio $\frac{S_n}{S_{n+1}}$ is :

The slope of velocity-time graph for motion with uniform velocity is equal to