Time taken by the projectile to reach from A to B is t. Then the distance AB is equal to :

1. $\frac{ut}{\sqrt{3}}$

2. $\frac{\sqrt{3}ut}{2}$

3. $\sqrt{3}ut$

4. 2ut

Three particles are moving with constant velocities $v_1 ,v_2$ and $v$ respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among $v_1 ,v_2$ and $v$ is:
                            
1. $v =v_1+v_2$
2. $v= \sqrt{v_{1} v_{2}}$
3. $v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}$
4. $v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}$

A body is thrown horizontally with a velocity $\sqrt{2gh}$ from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is:

(1) h

(2) $\frac{h}{2}$

(3) 2h

(4) $\frac{2h}{3}$

A particle starts from the origin at t=0 and moves in the x-y plane with a constant acceleration 'a' in the y direction. Its equation of motion is $y=b{x}^2$. The x component of its velocity (at t=0) will be:

1. variable

2. $\sqrt{\frac{2a}{b}}$

3. $\frac{a}{2b}$

4. $\sqrt{\frac{a}{2b}}$

A boat is sent across a river in perpendicular direction with a velocity of 8 km/hr. If the resultant velocity of boat is 10 km/hr, then velocity of the river is : 

(1) 10 km/hr

(2) 8 km/hr

(3) 6 km/hr

(4) 4 km/hr

A boat moves with a speed of $5$ km/h relative to water in a river flowing with a speed of $3$ km/h. Width of the river is $1$ km. The minimum time taken for a round trip will be:
1. $5$ min
2. $60$ min
3. $20$ min
4. $30$ min

A river is flowing from $W$ to $E$ with a speed of $5$ m/min. A man can swim in still water with a velocity of $10$ m/min. In which direction should the man swim so as to take the shortest possible path to go to the south:

If a particle moves in a circle describing equal angles in equal times, its velocity vector:

(1) remains constant.

(2) changes in magnitude.

(3) changes in direction.

(4) changes both in magnitude and direction.

A motorcyclist going round in a circular track at constant speed has:

(1) constant linear velocity

(2) constant acceleration

(3) constant angular velocity

(4) constant force