A particle is moving with velocity $\overrightarrow{\mathrm{v}}=\mathrm{k}(\mathrm{y}\hat{\mathrm{i}}+\mathrm{x}\hat{\mathrm{j}})$ where k is a constant. The general equation for the path will be:

1.	y = x2 + constant	2.	y2 = x2 + constant
3.	y = x + constant	4.	xy=constant

A body is thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:

1. $\sqrt{2}t$

2. $\left(1+\frac{1}{\sqrt{2}}\right)t$

3. $\frac{3t}{2}$

4. $\frac{t}{\sqrt{2}}$

Three particles are moving with constant velocities ${\mathrm{v}}_1,$ ${\mathrm{v}}_2$ 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 ${\mathrm{v}}_1,$ ${\mathrm{v}}_2$ and v is:
                                    
1.  $\mathrm{v}=$ ${\mathrm{v}}_1$ $+$ ${\mathrm{v}}_2$

2.  $\mathrm{v}=$ $\sqrt{{\mathrm{v}}_1{\mathrm{v}}_2}$

3.  $\mathrm{v}=\frac{{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1+{\mathrm{v}}_2}$

4.  $\mathrm{v}=$ $\frac{\sqrt{2}{\mathrm{v}}_1{\mathrm{v}}_2}{{\mathrm{v}}_1+{\mathrm{v}}_2}$

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 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. 

1. 30° with downstream

2. 60° with downstream

3. 120° with downstream

4. South

Certain neutron stars are believed to be rotating at about 1 rev/s. If such a star has a radius of 20 km, the acceleration of an object on the equator of the star will be:

In 1.0 s, a particle goes from point A to point B, moving in a semicircle of radius 1.0 m (see figure). The magnitude of the average velocity is:
                   

The angle turned by a body undergoing circular motion depends on the time as given by the equation, $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$. It can be deduced that the angular acceleration of the body is? 

1. θ₁

2. θ₂

3. 2θ₁

4. 2θ₂

A particle is moving eastwards with velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is?