Distance 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 car moving with a speed of $40 \mathrm{km} {\mathrm{h}}^{-1}$ is stopped in $2 \mathrm{m}$ distance when brakes are applied. If the speed be increased to $80 \mathrm{km} {\mathrm{h}}^{-1}$, the stopping distance would be:

A vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $\mathrm{d}\theta$. What will be the value of $\left|∆\overrightarrow{a}\right|$ and $∆a$, respectively?

The magnitudes of vectors $\overrightarrow{\mathrm{A}},\overrightarrow{\mathrm{B}}$ and $\overrightarrow{\mathrm{C}}$  are 3, 4 and 5 units respectively. What is the angle between $\overrightarrow{\mathrm{A}} and \overrightarrow{\mathrm{B}}$  if $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{C}}$?

If $\overrightarrow{r }=3t^2\hat{\mathrm{i}}+4t^2\hat{\mathrm{j}}+7\hat{\mathrm{k}}$ represents the position vector of a particle. In first $10 \mathrm{s}$, the distance traversed by the particle is,

If a man goes $10 \mathrm{m}$ towards north and $20 \mathrm{m}$ towards east, then his displacement is

The half life period of neutron is 13 minutes approximately. The intensity of neutron beam travelling in free space with a velocity of $30$ kilometre per second is reduced to half when it covers a distance of

A blind person, after walking $10$steps in one direction each of length $80 \mathrm{cm}$, turns randomly to the left or to right by $90°$. After walking a total of $40$ steps, the maximum displacement of the person from its starting point can be:

An aeroplane flies 400m north and 300m south and then flies 1200m upwards, then net displacement is

A farmer has to go $500 \mathrm{m}$ due north, $400 \mathrm{m}$ due east and $200 \mathrm{m}$ due south to reach his field. If he takes $20$ minutes to reach the field. What is the displacement from his house to the field?

The distance travelled by a particle starting from rest and moving with an acceleration $\frac{4}{3}{\text{m s}}^{-2}\text{,}$ in the third second is

A cyclist starts from the centre $\mathrm{O}$ of a circular park of radius $1 \mathrm{km}$, reaches the edge $\mathrm{P}$ of the park, then cycles along the circumference (clockwise)  and returns to the centre along $\mathrm{QO}$ as shown. If the round trip takes $10 \min$, what is the (a) net displacement, (b) average velocity and (c) average speed of the cyclist ? 

A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QO as shown. If the round trip takes 10 min, what is the (a) net displacement, (b) average velocity and (c) average speed of the cyclist (in km/hr)?

A hall has the dimensions $10\text{m}\times 10\text{m}\times 10\text{m}$. A fly starting at one corner ends up at diagonally opposite corner. The magnitude of its displacement is nearly :