A particle moving on a curved path possesses a velocity of 3 m/s towards the north at an instant. After 10 s, it is moving with speed 4 m/s towards the west. The average acceleration of the particle is-

1.	0.25 $\mathrm{m}/{\mathrm{s}}^2$, 37° south to east
2.	0.25 $\mathrm{m}/{\mathrm{s}}^2$, 37° west to north
3.	0.5 $\mathrm{m}/{\mathrm{s}}^2$, 37° east to north
4.	0.5 $\mathrm{m}/{\mathrm{s}}^2$, 37° south to west

A man can row a boat with a speed of 10 kmph in still water. The river flows at 6 kmph. If he crosses the river from one bank to the other along the shortest possible path, time taken to cross the river of width 1 km is:

1. 1/8 h

2. 1/4 h

3. 1/2 h

4. 1 h

A bus is going to the North at a speed of 30 kmph. It makes a 90° left turn without changing the speed. The change in the velocity of the bus is:

Two bullets are fired simultaneously horizontally and at different speeds from the same place. Which bullet will hit the ground first? (Air resistance is neglected)

An aeroplane flies \(400\) m north and then \(300\) m west and then flies \(1200\) m upwards. Its net displacement is:

 Select the incorrect statement:

A particle of mass 2 kg is moving in a circular path with a constant speed of 10 m/s. The change in the magnitude of velocity when a particle travels from P to Q will be: [assume the radius of the circle is 10/${\mathrm{\pi }}^2$]
         

To the captain of a ship A travelling with velocity $\overrightarrow{v_A}=(3\hat{i}-4\hat{j})$ km/h, a second ship B appears to have a velocity ${\overrightarrow{v}}_B=\left(5\hat{i}+12\hat{j}\right)$ km/h. What is the true velocity of the ship B?

1. $2\hat{i}+16\hat{j}$ $km/h$

2. $13\hat{i}+8\hat{j}$ $km/h$

3. $-2\hat{i}-16\hat{j}$ $km/h$

4. none of these

An object moves at a constant speed along a circular path in a horizontal XY plane with its centre at the origin. When the object is at x = –2 m, its velocity is –(4 m/s)$\hat{\mathrm{j}}$. What is the object's acceleration when it is at y = 2 m?

1. $-(8\mathrm{ m}/{\mathrm{s}}^2)$ $\hat{\mathrm{j}}$

2. $-(8\mathrm{ m}/{\mathrm{s}}^2)$ $\hat{\mathrm{i}}$

3. $-(4\mathrm{ m}/{\mathrm{s}}^2)$ $\hat{\mathrm{j}}$

4. $-(4\mathrm{ m}/{\mathrm{s}}^2)$ $\hat{\mathrm{i}}$

The position of a moving particle at time \(t\) is \(\vec{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.\) Its displacement during the time interval \(t=1\) s to \(t=3\) s will be: