Motion in a straight line practice · Medium

The position of a particle moving along $x$-axis varies with time $t$ as $x=4 t-t^2+1$. Find the time interval(s) during which the particle is moving along positive $x$-direction.

A point moves such that its displacement as a function of time is given by $x^3=t^3+1$. Its acceleration as a function of time $t$ will be

Assertion: The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.

Reason: Velocity is a vector quantity and speed is a scalar quantity.

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three second. The body has fallen for a time of:-

A body projected vertically upwards with a certain speed from top of a tower, reaches the ground in time $t_1.$ If it is projected vertically downwards with same speed from same point, it reach the ground in the time $t_2.$ Time required for it to reach the ground if it dropped from the same point and projected horizontally with same speed, respectively are

The ball is projected up from ground with speed 30 m/sec. What is the average velocity for time 0 to 4 sec?

Assertion: The slope of the velocity-time graph for an object in uniform motion is zero.

Reason: The velocity-time graph for uniform motion is parallel to velocity-axis.

A car moving on straight path, travels first half of distance with speed $20\, {~m} / {s}$ and another half of distance with speed $40 \,{~m} / {s}$, then average speed of the journey is

A wheel covers a distance of $9.5 \mathrm{~km}$ in 2000 revolutions. The diameter of the wheel is

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

For motion of an object along $x$-axis, the velocity $v$ depends on the position $x$ as $v=\left(2 x^2-x\right) \mathrm{m} / \mathrm{s}$, where $x$ is in $\mathrm{m}$. The acceleration of the object at $x=1 \mathrm{~m}$ will be

A stone thrown vertically upwards with a speed of $5 \mathrm{~m} / \mathrm{sec}$ attains a height $H_1$. Another stone thrown upwards from the same point with speed of $10 \mathrm{~m} / \mathrm{sec}$ attains a height $H_2$. The correct relation between $H_1$ and $H_2$ is:

A stone is thrown with an initial speed of 4.9 m/s from a bridge in vertically upward direction. It falls down in water after 2 sec. The height of the bridge is

The displacement x of a particle varies with time according
to the relation ) $x = \frac{a}{b}\left( {1 - {e^{ - bt}}} \right)$. Then select the false alternative.

A body moves in straight line with velocity $v_1$ for $1 / 3^{\text {rd }}$ time and for remaining time with $\mathrm{v}_2$. Find average velocity.

A particle travels 80 m with 5 m/s velocity, later it
continuous to travel 20 m in 9 sec. Find average
velocity

A particle moves in straight line with velocity $v_1$ and $v_2$ for time intervals which are in ratio $1:2.$ Find average velocity.

A Body moves 6 m north. 8 m east and 10 m vertically upwards, what is its resultant displacement from initial position

A particle starts from rest with constant acceleration. The ratio of magnitude of displacement in $n^{\text {th }}$ second to that of in $n$ second, is

The relation between $t$ and distance $x$ is $t=a x^2+b x$ where $a$ and $b$ are constants. Express the instantaneous acceleration in terms of instantaneous velocity.

A body is thrown up with a velocity $100 \mathrm{~ms}^{-1}$. It travels $5 \mathrm{~m}$ in the last second of its journey. If the same body is throw up with a velocity $200 \mathrm{~ms}^{-1}$, how much distance (in metre will it travel in the last second $\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$ ?

Two bodies of different masses are dropped simultaneously from the top of a tower. If air resistance is proportional to the mass of the body. Then

Assertion : position-time graph of a body moving uniformly in a straight line parallel to position axis. Says body is at rest.

Reason : The slope of position-time graph in a uniform motion gives the velocity of an object.

The relative velocity $\mathrm{V}_{\mathrm{AB}}$ or $\mathrm{V}_{\mathrm{BA}}$ of two bodies $\mathrm{A}$ and $\mathrm{B}$ may be

I. greater than velocity of body A

II. greater than velocity of body B

III. less than the velocity of body A

IV. less than the velocity of body B

From the top of tower, a particle is thrown vertically downwards with a velocity of $10 \mathrm{~m} / \mathrm{s}$. The ratio of the distances covered by it in the 3rd and 2nd seconds of the motion is : (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ) :

The area under acceleration-time graph gives

Assertion: The average speed of a body over a given interval of time is equal to the average velocity of the body in the same interval of time if a body moves in a straight line in one direction.
Reason: Because in this case distance travelled by a body is equal to the displacement of the body.

A stone is dropped from a rising balloon at a height of $76 \mathrm{~m}$ above the ground and reaches the ground in $6 \mathrm{~s}$. What was the velocity of the balloon when the stone was dropped? [Take ${g}=10 \mathrm{~m} / \mathrm{s}^2$]

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

The displacement of the particle varies with time according to the relation $x = \frac{k}{b}\left[ {1 - {e^{ - bt}}} \right].$ Then the velocity of the particle is