Position Vector, Displacement, Velocity and Acceleration

A train is moving eastward at $10 \mathrm{m}/\sec$. A waiter is walking eastward at $1.2\mathrm{m}/\sec$ and a fly is charging towards the north across the waiter's tray at $2 \mathrm{m}/\mathrm{s}$. What is the velocity of the fly relative to Earth. 

The vector joining the points $A\left(1, 1,-1\right)$ and $B\left(2,-3, 4\right)$ and pointing from $A$ to $B$ is

At which point of a projectile motion, acceleration and velocity are perpendicular to each other?

A particle has an initial velocity of $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ and an acceleration of $0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}$. Its speed after $10 \mathrm{s}$ is

Derive the expression for angle between acceleration vector and one of its component vectors when components are given.

For motion in two or three dimensions, velocity and acceleration vectors may have any angle between 0° and _____ between them.

A particle starts form the origin at $t=0$, with a velocity $5.0 \hat{i} {\mathrm{ms}}^{-1}$. When a certain force is applied on it, the position of the particle is $r\left(t\right)=\left(5.0t+1.5t^2\right) \hat{i}+1.0t^2 \hat{j}$. What is the velocity of the particle at $t=6 \mathrm{s}$?

The position of the particle is given by $r=3.0t \hat{i}+2.0t^2 \hat{j}+5.0 \hat{k}$ where $t$ is in seconds. Find the magnitude and direction of the $V\left(t\right)$ at $t=1.0 \mathrm{s}$.

A passenger arriving in a new town wishes to go from the station to a hotel located $10 \mathrm{km}$ away on a straight road from the station. A dishonest cabman takes him along a circuitous path $23 \mathrm{km}$ long and reaches the hotel in $28 \min$. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? 

A particle starts from the origin with an initial velocity $\overrightarrow{v}=\left(3.0\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$ and a constant acceleration $\overrightarrow{a}=\left(-0.5\hat{\mathrm{i}}-1.0\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-2}$. The velocity of the particle when it reaches its maximum y coordinate is

An object is moving in a plane and its trajectory $\overrightarrow{r}\left(t\right)$ (in meter) is given by, $\overrightarrow{r}\left(t\right)=\left(3t^2+2t\right)\hat{\mathrm{i}}+2t\hat{\mathrm{j}}$, where t is time (in second). The angle that the velocity vector makes with the $X$ -axis at $t=0$.

A particle is moving along a circular path of radius $5 \text{m}$ with a uniform speed of $5 {\text{ms}}^{-1}$.What will be the average accelaration when the particle completes half revolution ?

One of the rectangular components of an acceleration of $8\mathrm{}\mathrm{m}\mathrm{}{\mathrm{s}}^{-2}$ is $4\mathrm{}\mathrm{m}\mathrm{}{\mathrm{s}}^{-2}$. Calculate the other component.

What is the component of the gravitational acceleration parallel to a hill that makes an angle of $15°$ with the horizontal?

A force is inclined at $50°$ to the horizontal. If its rectangular component in the horizontal direction be $50\mathrm{}\mathrm{N}$, find the magnitude of the force and its vertical component.

Aeroplane is coming from north at some height from ground when aeroplane is just above the person; person hears the second coming from north making angle ${60}^o$ with horizontal. Find speed of aeroplane

An ant starting from corner $A$ of a cuboid of length $L$, breadth $\mathrm{\text{B}}$and height $H$ wishes to reach the corner $C$ in the shortest possible time. It is capable of moving with a velocity $V$. Find the minimum time in which it can get from $A$ to $C$.

Given $(H>L>B)$

A rod PQ of length $l$ is moving with ends remaining in contact with frictionless wall and floor. If at the instant, shown the velocity of end Q $2m/s$ towards negative direction of $x$ . The speed of end P will be