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

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 particle starts from the origin at t=0 and moves in the x-y plane with a 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) will be:

1. variable
2. \(\sqrt{\dfrac{2a}{b}}\)
3. \(\dfrac{a}{2b}\)
4. \(\sqrt{\dfrac{a}{2b}}\)

Three particles are moving with constant velocities \(v_1 ,v_2\) and \(v\) respectively as given in the figure. After some time, if all the three particles are in the same line, then the relation among \(v_1 ,v_2\) and \(v\) is:
                            
1. \(v =v_1+v_2\)
2. \(v= \sqrt{v_{1} v_{2}}\)
3. \(v = \frac{v_{1} v_{2}}{v_{1} + v_{2}}\)
4. \(v=\frac{\sqrt{2} v_{1} v_{2}}{v_{1} + v_{2}}\)