Speed and Velocity

The most probable, root-mean-square speeds and average velocity are in the ratio of _____ respectively (with three decimal places).

The motion of a particle is described by $\mathrm{x}={\mathrm{x}}_0(1-{\mathrm{e}}^{-\mathrm{kt}}) ; \mathrm{t}\ge 0,\mathrm{k}>0$. Find the initial velocity of the particle.

The position of an object moving along $x-$axis is given by $x=a+b{t}^2$, where $a=8.5 \mathrm{m} \text{and} b=2.5\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$ and $t$ is measured in seconds. The instantaneous velocity of the object at $t=2 \mathrm{s}$ is

A body moving along a straight line travels one third of the total distance with a speed of $3.0\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$. The remaining distance is covered with a speed of $4.0\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$ for half the time and $5.0\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$ for the other half of the time. The average speed during the motion is

The position of an object moving along x-axis is given by $\mathrm{x}=\mathrm{a}+\mathrm{b}{\mathrm{t}}^2$ , Where $\mathrm{a}=8.5\mathrm{ }\mathrm{m}$ and $\mathrm{b}=2.5\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$ and $\mathrm{t}$ is measured in seconds. The average velocity of the object between $\mathrm{t}=2\mathrm{ }\mathrm{s}\mathrm{ }$and $\mathrm{t}=4 \mathrm{s}$ is:

Which of the following statements are incorrect ?
$\left(\mathrm{i}\right)$ Average velocity is path length divided by time interval.
$\left(\mathrm{i}\mathrm{i}\right)$ In general, speed is greater than the magnitude of the velocity.
$\left(\mathrm{i}\mathrm{i}\mathrm{i}\right)$ A particle moving in given direction with a non-zero velocity can have zero speed.
$\left(\mathrm{i}\mathrm{v}\right)$ The magnitude of average velocity is the average speed.

What will be ratio of speed in first two seconds to the speed in next 4s?

The average speed of a group of 7 gas molecules having velocity $\left(6,\mathrm{ }4,\mathrm{ }2,\mathrm{ }0,\mathrm{ }–2,\mathrm{ }–4,\mathrm{ }–6\right)\mathrm{ }\mathrm{m}/\mathrm{s}$ is-

Assertion: Average velocity of a particle moving on curved path is never equal to instantaneous velocity of particle.
Reason: Neither magnitude nor direction of average velocity can be same as that of instantaneous velocity of particle which is moving on curved path.

Assertion: Magnitude of instantaneous velocity is equal to instantaneous speed.
Reason: Distance is nearly equal to displacement if displacement is very small.

Assertion: A body is momentarily at rest when it reverses the direction.

Reason: A body cannot have acceleration if its velocity is zero at a given instant of time.

Assertion: A body can have acceleration even if its velocity is zero at a given instant of time

Reason: A body is momentarily at rest when it reverses its direction of motion

A study of automobile speeds on a highway yielded the following data for a 1 hour period- Speed in $\mathrm{km} {\mathrm{h}}^{-1}$ and Number of cars (n)

(i) 40 kmph -10 cars

(ii) 45 kmph- 8 cars

(iii) 50 kmph- 15 cars

(iv) 55 kmph- 10 cars

(v) 60 kmph- 12 cars

Which of the following is/are correct-

A cyclist starts from the centre $O$ of a circular park of radius one kilometre, reaches the edge $P$ of the park, then cycles along the circumference and returns to the centre along $QO$ as shown in the figure. If the round trip takes ten minute, the net displacement and average speed of the cyclist (in $\mathrm{m}$ and $\mathrm{km} {\mathrm{h}}^{-1}$, respectively) is

A particle is moving in a straight line along $x-$axis, its position is given by,$x=2t^2+2t+4$, where$x$ is in metre and $t$ in second, the acceleration of the particle is

A car travels equal distances in the same direction with velocities $60\mathrm{k}\mathrm{m}{\mathrm{h}}^{-1}$, $20 \mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$ and 10 $\mathrm{k}\mathrm{m}\mathrm{ }{\mathrm{h}}^{-1}$respectively. The average velocity of the car over the whole journey of motion is

A body starts from origin and moves along $x$-axis such that at any instant velocity is $v_t=4t^3-2t$ where $t$ is in second and $v_t$ in $\mathrm{m}{\mathrm{s}}^{-1}$. The acceleration of the particle when it is 2m from the origin is

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?

A car moves from $X \mathrm{t}\mathrm{o}\mathrm{ }Y$ with a uniform speed $v_u$ and returns to $Y$ with a uniform speed $v_d.$The average speed for this round trip is

A body of mass $m$ moving along a straight line covers half the distance with a speed of $2 {\mathrm{m} \mathrm{s}}^{-1}.$ The remaining half of distance is covered in two equal time intervals with a speed of $3 {\mathrm{m} \mathrm{s}}^{-1} \text{and}\mathrm{ }\mathrm{ }5\mathrm{ }{\mathrm{m} \mathrm{s}}^{-1}$ respectively. The average speed of the particle for the entire journey is