Instantaneous Velocity and Speed

A particle goes from $A$ to $B$ with a speed of $40 \mathrm{km} {\mathrm{h}}^{-1}$ and $B$ to $C$ with a speed of $60 \mathrm{km} {\mathrm{h}}^{-1}$. If $AB=6\hspace{0.17em}BC$, the average speed in $\mathrm{km} {\mathrm{h}}^{-1}$ between $A$ and $C$ is

A car moves a distance of 200 m. It covers the first half of the distance at speed  $40\frac{km}{hr}$  and the second half of distance at speed v. The average speed is  $48\frac{km}{hr}$ . Find the value of v

A bus travelling the first one third distance at a speed of  $10 \mathrm{km} {\mathrm{h}}^{-1}$, the next one third at  $20 \mathrm{km} {\mathrm{h}}^{-1}$ and the last one – third at  $60 \mathrm{km} {\mathrm{h}}^{-1}$. The average speed of the bus is

A car covers the first half of the distance between two places at  $40\frac{km}{h}$  and other half at  $60\frac{km}{h}$ . The average speed of the car is

The displacement $x$ of particle moving in one dimension, under the action of a constant force is related to the time $t$ by the equation  $t=\sqrt{x}+3$ where $x$ is in meters and $t$ in seconds. Find the displacement of the particle when its velocity is zero.

The coordinates of a moving particles at any time $t$ are given by  $x=\alpha t^3$ and $y=\beta t^3$ . The speed of the particle at time $t$ is given by –

The coordinates of a moving particles at any time $t$ are given by  $x=\alpha t^3$ and $y=\beta t^3$ . The speed of the particle at time $t$ is given by –

In $1.0 \mathrm{s}$, a particle goes from point $A$ to point $B$, moving in a semicircle of radius $1.0 \mathrm{m}$ (see figure). The magnitude of the average velocity is

A vehicle travels half the distance with speed $v$ and the remaining distance with speed $2v$. Its average speed is:

The distance travelled by an object in time $t$ is given by $s=\left(2.5\right)t^2$ . The instantaneous speed of the object at$t=5 \mathrm{s}$ will be :

As shown in the figure, a particle is moving with constant speed $\pi \mathrm{m} {\mathrm{s}}^{-1}$. Considering its motion from $A$ to $B$, the magnitude of the average velocity is:

A person travels $x$ distance with velocity $v_1$ and then $x$ distance with velocity $v_2$ in the same direction. The average velocity of the person is $v$, then the relation between $v, v_1$ and $v_2$ will be

If position of particle is changing with time as $r=t^2-2t \left(\mathrm{m}\right)$. Find the velocity at $t=2 \mathrm{s}.$

An object moves $x$ distance with speed $v_1$ and next $x$ distance with speed $v_2$. The average velocity $v$ is related to $v_1$ and $v_2$ as

A particle moves from A to B via C with uniform speed $\pi \mathrm{m} {\mathrm{s}}^{-1}$. Average velocity during the journey is equal to

The path of a particle is given by the expression $y= at+b{t}^2$, where $a$ and $b$ are constants. $y$ is the displacement at time $t$. Find its velocity at any instant.