A particle starts from the origin at t=0 and moves in the x-y plane with 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) is:

1. variable

2. $\sqrt{\frac{2a}{b}}$

3. $\frac{a}{2b}$

4. $\sqrt{\frac{a}{2b}}$

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

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

1. 10 km/hr

2. 8 km/hr

3. 6 km/hr

4. 4 km/hr

A train is moving towards the east and a car is along the north at the same speed. The observed direction of the car to the passenger on the train is:
1. East-north direction
2. West-north direction
3. South-east direction
4. None of these

If the body is moving in a circle of radius r with a constant speed v, its angular velocity is:

1. v²/r

2. vr

3. v/r

4. r/v

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 moves with constant angular velocity in a circle. During the motion its:

The angular speed of a flywheel making 120 revolutions/minute is: 

1. $2\pi rad/s$

2. $4{\pi }^{2}rad/s$

3. $\pi rad/s$

4. $4\pi rad/s$

The angle turned by a body undergoing circular motion depends on time as $\theta ={\theta }_0+{\theta }_{1}t+{\theta }_2{t}^2$. Then the angular acceleration of the body is 

(1) θ₁

(2) θ₂

(3) 2θ₁

(4) 2θ₂