A particle has initial velocity $\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}\right)$ and has acceleration $\left(0.4\hat{\mathrm{i}}+0.3\hat{\mathrm{j}}\right)$. Its speed after 10 s:

1. 7 units

2. $7\sqrt{2}$ units

3. 8.5 units

4. 10 units

What determines the nature of the path followed by the particle?

1. Speed only

2. Velocity only

3. Acceleration only

4. None of these

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

1. \(10\ \text{km/hr}\)

2. \(8\ \text{km/hr}\) 

3. \(6\ \text{km/hr}\) 

4. \(4\ \text{km/hr}\) 

A boat moves with a speed of \(5\ \text{km/h}\) relative to water in a river flowing with a speed of \(3\ \text{km/h}\) and having a width of \(1\ \text{km}\). The minimum time taken for a round trip (returning to the initial point) is:

1. \(5\ \text{min}\)

2. \(60\ \text{min}\)

3. \(20\ \text{min}\)

4. \(30\ \text{min}\)

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 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

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 a constant speed has:

1. constant linear velocity.

2. constant acceleration.

3. constant angular velocity.

4. constant force.

A particle \(P\) is moving in a circle of radius \(a\) with a uniform speed \(v\). \(C\) is the centre of the circle and \(AB\) is a diameter. When passing through \(B\) the angular velocity of \(P\) about \(A\) and \(C\) are in the ratio:

1. \(1 : 1\)

2. \( 1 : 2\)

3. \(2 : 1\)

4. \(4 : 1\)

The angular speed of a flywheel making \(120\ \text{revolutions/minute }\)is: 

1. \(2 𝜋\ \text{𝑟𝑎𝑑/𝑠}\) $\mathrm{}$

2. \(4 𝜋^2\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

3. \(𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$$

4. \(4 𝜋\ \text{𝑟𝑎𝑑/𝑠}\)$\mathrm{}$

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

1. \(20×10^8\ \text{m/s}^2\)

2. \(8×10^5\ \text{m/s}^2\)

3. \(120×10^5\ \text{m/s}^2\) $\mathrm{}$

4. \(4×10^8\ \text{m/s}^2\)$\mathrm{}$