Position, Path Length and Displacement

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.

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.

Define motion.

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 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

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

In one second, a particle goes from point A to B moving in along circle shown in figure. The magnitude of its average velocity is

If position of a particle is $x= 5t^2-20t+2$, find distance and displacement at $t= 4 \mathrm{s}$.

The combined frictional and air resistance on a bicyclist has the force$F=av$, where v is his velocity and $a=4 N s m^{-1}$. At maximum effort, the cyclist can generate $400 watts$ propulsive power. What is his maximum speed (in $m s^{-1}$) on level ground with no wind? 

Figure shows the time-displacement curve of the particles P and Q. Which of the following statement is correct?

A body is moving along the circumference of a circle of radius R and completes half of the revolution. Then, the ratio of the displacement to distance is 

An insect can crawl on the floor. If it starts crawling from one corner of a cubical room of slde '$a$' Minimum distance it would crawl to raech the furthermost corner in the room.

The position time graph for a particle moving on $x$-axis is shown here. Choose correct statement.

A frog takes $5$ leaps in forward direction and $2$ leaps backward. A pot hole is $22 \mathrm{cm}$ a head of the frog. If the distance covered in $1$ leap is $1 \mathrm{cm}$. Find the distance travelled by frog before it falls in the pothole.

An aeroplane is flying from city $A$ to city $B$ along path $1$ . The path $1$ is a circular arc whose centre coincides with the centre of the Earth. Another aeroplane is flying along path $2$ from $A$ to $B$. The path $2$ is circular arc whose centre is at $C.O$ is the centre of the Earth. Then,

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A person runs along a circular path of radius $5 \mathrm{m}$. If he completes half of the circle find the magnitude of the displacement vector. How far the person ran?

A motorist travelled from town A To Town B at an average speed of $54 \mathrm{km}/\mathrm{hour}$. On his return journey, he travelled his average speed with $60 \mathrm{km}/\mathrm{hour}$. If the total time taken is $19/2 \mathrm{hours}$, find the distance between the two towns.

Let ${\mathrm{x}}_1$ and ${\mathrm{x}}_2$ be the positions of an object at time ${\mathrm{t}}_1$ and ${\mathrm{t}}_2$. Then, its displacement, denoted by A, in time $\mathrm{\Delta t} =\mathrm{B}$, is given by the difference between the C and D position.
Here A,B,C and D refer to 

The velocity-time graph of a particle in linear motion is shown. Both $v$ and $t$ are in SI units. What is the displacement of the particle from the origin after $8$ second.