Distance and Displacement

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 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 particle moves in a circle of radius $R.$ Find its displacement and the distance covered for half the period of its revolution.

A boy moves from A to B through $5 \mathrm{cm}$, B to C through $12 \mathrm{cm}$ and again from C to D through $5 \mathrm{cm}$. Find his displacement.

A particle moving along the path $y=x^2$, from $x=0 \mathrm{m}$ to $x=2 \mathrm{m}$. Then the distance travelled by the particle 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 :

A disc is rolling without slipping on a surface. The radius of the disc is $R.$ At $t=0,$ the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is

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:

Two particles move from A to C and A to D on a circle of radius R and diameter AB. If the time taken by both particles are the same, then the ratio of magnitudes of their average velocities is