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 (2i + 3j) m/s. Its velocity (in m/s) at point B is:


1.  -2i+3j

2.  -2i-3j

3.   2i-3j

4.  2i+3j

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) $7 \mathrm{m}/{\mathrm{s}}^2$                                             

(2) $\sqrt{7} \mathrm{m}/{\mathrm{s}}^2$

(3) $5 \mathrm{m}/{\mathrm{s}}^2$                                             

(4) $1 \mathrm{m}/{\mathrm{s}}^2$

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 km/hr, a train appears to move towards north with a velocity of $25\sqrt{3}$ km/hr. The actual velocity of the train will be

1. 25 km/hr

2. 50 km/hr

3. 5 km/hr

4. $5\sqrt{3}$ km/hr

A particle moves towards east with velocity 5 m/s. After 10 seconds its direction changes towards north with same velocity. The average acceleration of the particle is 

1. Zero

2. $\frac{1}{\sqrt{2}}m/s^{2}N-W$

3. $\frac{1}{\sqrt{2}}m/s^{2}N-E$

4. $\frac{1}{\sqrt{2}}m/s^{2}S-W$

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

1. 16 sec

2. 12 sec

3. 10 sec

4. 8 sec

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

1. 2h

2. 2h 40 min

3. 1h 20 min

4. Cannot be estimated with the information given