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A car is moving at a speed of 30 m/s on a horizontal circular track of radius of 300 m. This speed is increasing at a rate of 4 $\mathrm{m}/{\mathrm{s}}^2$. Total acceleration of the car is:
(1) 5 $\mathrm{m}/{\mathrm{s}}^2$
(2) 7 $\mathrm{m}/{\mathrm{s}}^2$
(3) 1 $\mathrm{m}/{\mathrm{s}}^2$
(4) 3 $\mathrm{m}/{\mathrm{s}}^2$

The radius vector of a particle moving on a circle is given by $\overrightarrow{\mathrm{r}} = \mathrm{AcosBt}\hat{\mathrm{i}} + \mathrm{AsinBtj}\stackrel{}{^}$ (A and B are constants). The radius of the circle and speed of the particle, respectively, are
1.  A, AB
2.  $\mathrm{A}, \frac{{\mathrm{A}}^2}{\mathrm{B}}$
3.  B, AB
4.  $\mathrm{B}, \frac{{\mathrm{A}}^2}{\mathrm{B}}$

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

For a particle in a non-uniform accelerated circular motion 
(1) Velocity is radial and acceleration is transverse only
(2) Velocity is transverse and acceleration is radial only
(3) Velocity is radial and acceleration has both radial and transverse components
(4) Velocity is transverse and acceleration has both radial and transverse components

If the equation for the displacement of a particle moving on a circular path is given by \(\theta = 2t^3 + 0.5\) where θ is in radians and t in seconds, then the angular velocity of the particle after 2 sec from its start is:
1. 8 rad/sec
2. 12 rad/sec
3. 24 rad/sec
4. 36 rad/sec

What is the value of linear velocity if \(\overset{\rightarrow}{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}\) and \(\overset{\rightarrow}{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}\)  :