Motion in a straight line practice · Mixed difficulty

The engine of a train can impart a maximum acceleration of $1\mathrm{m}{\mathrm{s}^{ - 2}}$ and the brakes can give a maximum retardation of $\mathrm{3m}{\mathrm{s}^{ - 2}}$ . The least time during which a train can go from one place to the other place at a distance of 1.2 km is nearly

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.

The co-ordinates of a moving particle any time “$t$” are given by $x = \alpha {t^3}\,\,\& \,\,y = \beta {t^3}.$ The speed of the particle at time $t = 2\,\,\sec$

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

A particle moves 200 cm in the first 2s and 220 cm in the next 4s with uniform deceleration. The velocity of the particle at the end of 7s is

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.

A ball thrown vertically upwards with an initial velocity of 2.4 m/s returns in 4 s. The total displacement of the ball is

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

A ball dropped onto the floor from a height of 40 m and rebounds of a height of 10 m. If the ball is in contact with the floor of 0.02 s, its average acceleration during contact is

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

A point moves with a uniform acceleration and $v_1, v_2, v_3$ denote the average velocities in three successive intervals of time $t_1, t_2, t_3$. Which of the following relations is correct?

A body $A$ is dropped vertically from the top of a tower. If another identical body $B$ is projected thrown from the same point at the same instant, then

A particle is moving on a straight line path with constant acceleration directed along the direction of instantaneous velocity. Which of the following statements are false about the motion of particle?

An elevator car whose floor to ceiling distance is $2.7 \mathrm{~m}$ starts ascending with a constant acceleration of $1.2 \mathrm{~ms}^{-2} .2 \mathrm{~s}$ after the start, a bolt falls from the ceiling of the car. The free fall time of the bolt is (Take, $g=9.8 \mathrm{~ms}^{-2}$ )

Assertion: The actual distance covered by an object in a given time interval can be equal to or greater than the magnitude of the displacement.

Reason: The distance covered is a scalar quantity, while the displacement is a vector quantity.

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?

Let $\vec{v}$ and $\vec{a}$ denote the velocity and acceleration respectively of a body in one dimensional motion. Then correct option is

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

Which of the following statements is true for a car moving on the road?

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

The co-ordinates of a particle moving in $x-y$ plane are given by: $x=2+4 t, y=3 t+8 t^2 \text {.}$The motion of the particle 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 block slides down a slope of angle $\theta$ with constant velocity. It is then projected up with a velocity of $10\,m{s^{ - 1}}\,$, $g = 10\,m{s^{ - 2}}$ and $\theta = 30^\circ$. The maximum distance it can go up the plane before coming to stop is

The velocity-time graph of particle comes out to be a non-linear curve. The motion is