Motion in a straight line practice · Medium

Two particles start form the same point with different speeds, but one moves along $y=a \sin \omega x$ and the other moves along curve $y=a \cos \omega x$ then

Water drops fall at regular intervals from a tap which is 5 m above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant

A boggy of uniformly moving train is suddenly detached from train and stops after covering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation

Statement-I: In successive time intervals if the average velocities of a particle are equal then the particle must be moving with constant velocity.
Statement-II: When a particle moves with uniform velocity, its displacement always increases with time.

Assertion: If displacement is a linear function of time, its average and instantaneous velocity will be same.
Reason: If the acceleration of a moving particle is zero, the particle moves linearly.

Free fall of an object (in vacuum) is a case of motion with

A train accelerates from rest at a constant rate α for distance ${x_1}$ and time ${t_1}$. After that it retards to rest at constant rate $\beta$ for distance ${x_2}$ and time ${t_2}$. Then it is found that

Consider the following statements and select the incorrect statements.

I. The magnitude of instantaneous velocity of a particle is equal to its instantaneous speed

II. The magnitude of the average velocity in an interval is equal to its average speed in that interval.

III. It is possible to have a situation in which the speed of the particle is never zero but the average speed in an interval is zero.

IV. It is possible to have a situation in which the speed of particle is zero but the average speed is not zero.

An object is moving in the $x-y$ plane with the position as a function of time given by $\vec{r}=x(t) \hat{i}+y(t) \hat{j}$. Point $O$ is at $x$ $=0, y=0$. The object is definitely moving towards $O$ when

The location of a particle has changed. What can we say about the displacement and the distance covered by the particle?

Which of the following is not a derived quantites?

A particle moves with constant acceleration and ${v_1},{v_2}$ and ${v_3}$ denote the average velocities in the three successive interval ${t_1},{t_2}$ and ${t_3}$ of time. Which of the following relations is correct?

If the position vector of a particle is $\vec{r}=3 t \hat{i}-4 \hat{j}+\hat{k}$, the particle will be -

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

What determines the nature of the path followed by the particle

A truck and a car are moving with equal velocity. On applying the brakes both will stop after certain distance, then

In the above question, the nearest distance between the two persons is

For a body moving with relativistic speed, if the velocity is doubled, then

A body completes a circular path of radius R in 12 S. The ratio of the magnitude of displacement to the distance travelled by it in 3 S is $\left[ {\pi = \frac{{22}}{7}} \right]$

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

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

Essential characteristic of equilibrium is

A particle starts from rest, acceleration at $2\;m/{s^2}$ for 10 s and then goes with constant speed for 30 s and then decelerates at $4\;m/{s^2}$ till it stops. What is the distance travelled by it

Acceleration of a particle changes when

The average acceleration vector for a particle having a uniform circular motion is

Three ships A, B and C are in motion. The motion of A as seen by B is with speed V towards the north-east. The motion of B as seen by C is with speed V towards the north-west. Then, as seen by A, C will be moving towards the

Assertion: The relative velocity between any two bodies moving in opposite direction is equal to sum of the
velocities of two bodies.

Reason: Sometimes relative velocity between two bodies is equal to difference in velocities of the two.

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

A bullet is fired with a speed of 1000 m/sec in order to hit a target 100 m away. If $g = 10\;m/{s^2}$, the gun should be aimed

A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distances travelled by the body in the first second and the seventh second is