A particle moves in east direction with $15 \,m/sec$. for $2\, sec$ then moves northward with $5\, m/sec$. for $8 \,sec$. then average velocity of the particle is

- A
$5\, m/sec\,$ due $E -37 -N$

- B
$5\, m/sec\,$ due $N -37 -E$

- C
$7\, m/sec\,$ due $S -37 -W$

- D
$10\, m/sec\,$ due $N -37 -E$

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $v$ and other with a uniform acceleration $a.$ If $\alpha$ is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by

A man wants to reach from $A$ to the opposite corner of the square $C$. The sides of the square are $100\, m$. A central square of $50\, m\,\times \,50\, m$ is filled with sand. Outside this square, he can walk at a speed $1\,ms^{-1}$. In the central square, he can walk only at a speed of $v\,ms^{-1}$ $(v < 1)$. What is smallest value of $v$ for which he can reach faster via a straight path through the sand than any path in the square outside the sand ?

In the graph shown in figure, which quantity associated with projectile motion is plotted along $y$-axis?

A mosquito is moving with a velocity $\overrightarrow{ v }=0.5 t ^{2} \hat{ i }+3 t \hat{ j }+9 \hat{ k }\, m / s$ and accelerating in uniform conditions. What will be the direction of mosquito after $2 \,s$ ?

- [JEE MAIN 2021]

A particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

- [JEE MAIN 2019]