The angle turned by a body undergoing circular motion depends on the time as given by the equation, \(\theta = \theta_{0} + \theta_{1} t + \theta_{2} t^{2}\). It can be deduced that the angular acceleration of the body is? 
1. \(\theta_1\)
2. \(\theta_2\)
3. \(2\theta_1\)
4. \(2\theta_2\)

A particle is moving eastwards with velocity of \(5\) m/s. In \(10\) seconds the velocity changes to \(5\) m/s northwards. The average acceleration in this time is?

A vector $\overrightarrow{a}$ is turned without a change in its length through a small angle $d\theta .$ The value of $\left|\Delta \overrightarrow{a}\right|$ and $\Delta a$ are, respectively:

A particle is moving such that its position coordinates \((x,y)\) are \((2\) m, \(3\) m) at time \(t=0,\)  \((6\) m, \(7\) m) at time \(t=2\) s and   \((13\) m, \(14\) m) at time \(t=5\) s. Average velocity vector \((v_{avg})\) from \(t=0\) to \(t=5\) s is:

The coordinates of a moving particle at a time \(t\), are given by, \(x= 5\sin 10t, y = 5\cos 10t\). It can be deduced that the speed of the particle will be:

What determines the nature of the path followed by a particle:
1. Speed
2. Velocity
3. Acceleration
4. Both (2) and (3)

A swimmer swims a distance d upstream in \(4\) s and swims an equal distance downstream in \(2\) s. The ratio of swimmer's speed in still water to the speed of river water will be:

In \(1.0~\text{s}\), a particle goes from point \(A\) to point \(B\), moving in a semicircle of radius \(1.0~\text{m}\) (see figure). The magnitude of the average velocity is:

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

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 of \(10\) m/min. In which direction should the man swim so as to take the shortest possible path to go to the south: