The \(x\) and \(y\) coordinates of the particle at any time are \(x = 5t-2t^2\) and \(y=10t\) respectively, where \(x\) and \(y\) are in metres and \(t\) is in seconds. The acceleration of the particle at \(t=2\) s is:
1. \(0\) m/s²
2. \(5\) m/s²
3. \(-4\) m/s²
4. \(-8\) m/s²

A ship A is moving Westwards with a speed of 10 km h^-1 and a ship B 100 km South of A, is moving Northwards with a speed of 10 km h^-1. The time after which the distance between them becomes shortest is

1., h
2. 5h
3. 5$\sqrt{2}$h
4. 10$\sqrt{2}$h

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:
      
1. \(-2\hat i+3\hat j~\)
2. \(-2\hat i-3\hat j~\)
3. \(2\hat i-3\hat j~\)
4. \(2\hat i+3\hat j~\)

A body is moving with velocity 30 m/s towards east. After 10 s its velocity becomes 40 m/s towards north. The average acceleration of the body is

(1) $7<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$                                             

(2) $\sqrt{7}<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$

(3) $5<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$                                             

(4) $1<mspace\; width="1em"></mspace>\mathrm{m}/{\mathrm{s}}^2$

A missile is fired for maximum range with an initial velocity of 20 m/s. If g=10 $\mathrm{m}/{\mathrm{s}}^2$, the range of the missile is:

1. 50 m                                                          2. 60 m

3. 20 m                                                          4. 40 m

A projectile is fired at an angle of 45$°$ with the horizontal. The elevation angle $\alpha$ of the projectile at its highest point as seen from the point of projection is:

1. 60$°$                                           2. ${\tan }^{-1}\left(\frac{1}{2}\right)$

3. ${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$                               4. $45°$

To a person going eastward in a car with a velocity of \(25\ \text{ km/hr}\), a train appears to move towards the north with a velocity of \(25\sqrt3\ \text{ km/hr}\). The actual velocity of the train will be:

1. \(25\ \text{ km/hr}\)

2. \(50\ \text{ km/hr}\)

3. \(5\ \text{ km/hr}\)

4.  \(5\sqrt3\ \text{ km/hr}\)$\mathrm{}$

A particle moves towards the east with a velocity \(5\ \text{m/s}\). After \(10\) seconds its direction changes towards the north with the same velocity. The average acceleration of the particle is:

1. Zero

2. \(\dfrac{1}{\sqrt{2}}\,m/s^2\ \text{N-W}\)

3. \(\dfrac{1}{\sqrt{2}}\,m/s^2\ \text{N-E}\)

4. \(\dfrac{1}{\sqrt{2}}\,m/s^2\ \text{S-W}\)

A \(120\ \text{m}\) long train is moving towards west with a speed of \(10\ \text{m/s}\). A bird flying towards east with a speed of \(5\ \text{m/s}\) crosses the train. The time taken by the bird to cross the train will be:

1. \(16\ \text{s}\)

2. \(12\ \text{s}\)

3.  \(10\ \text{s}\)

4. \(8\ \text{s}\)

A boat takes two hours to travel \(8\ \text{km}\) and back in still water. If the velocity of water is \(4\ \text{km/h}\), the time taken for going upstream \(8\ \text{km}\) and coming back is:

1. \(2\ \text{h}\)

2. \(2\ \text{h}\ 40\ \text{min}\)

3. \(1\ \text{h}\ 20\ \text{min}\)

4. Cannot be estimated with the information given