Two particles \({A}\) and \({B}\), move with constant velocities \(\vec{v}_1\) and \(\vec{v}_2\) respectively. At the initial moment, their position vectors are \(\vec{r}_1\) and \(\vec r_2\) respectively. The conditions for particles \({A}\) and \({B}\) for their collision will be:

1.	\(\dfrac{\vec{r}_1-\vec{r}_2}{\left|\vec{r}_1-\vec{r}_2\right|}=\dfrac{\vec{v}_2-\vec{v}_1}{\left|\vec{v}_2-\vec{v}_1\right|}\)
2.	\(\vec{r}_1 \cdot \vec{v}_1=\vec{r}_2 \cdot \vec{v}_2\)
3.	\(\vec{r}_1 \times \vec{v}_1=\vec{r}_2 \times \vec{v}_2\)
4.	\(\vec{r}_1-\vec{r}_2=\vec{v}_1-\vec{v}_2\)

The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\text{m/s}.\) Its velocity (in m/s) at the point \(B\) is:
              

A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

A missile is fired for a maximum range with an initial velocity of \(20~\text {m/s}.\) If \(g=10~\text{m/s}^2,\) then the range of the missile will be:

A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:

1.  $2\mathrm{mv}$

2.  $\mathrm{mv}/\sqrt{2}$

3.  $\mathrm{mv}\sqrt{2}$

4.  zero

A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are ($\sqrt{3}$, \(3).\) The path of the particle makes an angle of __________ with the \(x\)-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)

For a projectile projected at angles \((45^{\circ}-\theta)\) and \((45^{\circ}+\theta)\), the horizontal ranges described by the projectile are in the ratio of:
1. \(1:1\)
2. \(2:3\)
3. \(1:2\)
4. \(2:1\)

A car turns at a constant speed on a circular track of radius \(100~\text m,\) taking \(62.8~\text s\) for every circular lap. The average velocity and average speed for each circular lap, respectively, is: