A particle moves so that its position vector is given by \(r=\cos \omega t \hat{x}+\sin \omega t \hat{y}\) where \(\omega\) is a constant.  Based on the information given, which of the following is true?

1.	Velocity and acceleration, both are parallel to r.
2.	Velocity is perpendicular to r and acceleration is directed towards the origin.
3.	Velocity is not perpendicular to r and acceleration is directed away from the origin.
4.	Velocity and acceleration, both are perpendicular to r.

A particle has an initial velocity (\(2\mathrm{i}+3\mathrm{j}\)) and an acceleration (\(0.3\mathrm{i}+0.2\mathrm{j}\)). The magnitude of velocity after 10 s will be:
1. \(9 \sqrt{2} ~\text{units} \)
2. \(5 \sqrt{2} ~\text{units} \)
3. \(5 ~\text{units} \)
4. \(9~\text{units} \)

A particle moves in the x-y plane according to rule $\mathrm{x}=\mathrm{asin\omega t}$ and $\mathrm{y}=\mathrm{acos\omega t}$. The particle follows:

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, \(y=bx^{2}.\) The \(x\) component of its velocity is:
1. variable
2. \(\sqrt{\frac{2a}{b}}\)
3. \(\frac{a}{2b}\)
4. \(\sqrt{\frac{a}{2b}}\)

The horizontal range of a projectile is $4\sqrt{3}$ times its maximum height. Its angle of projection will be:

1. 45°

2. 60°

3. 90°

4. 30°

A cricketer can throw a ball to a maximum horizontal distance of 100 m. With the same effort, he throws the ball vertically upwards. The maximum height attained by the ball is 

1. 100 m

2. 80 m

3. 60 m

4. 50 m

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle $\left(\frac{\pi }{2}-\theta \right)$with the horizontal, it reaches maximum height H₂. The relation between the horizontal range of the projectile R and H₁ & H₂ is: 

Four bodies P, Q, R and S are projected with equal velocities having angles of projection 15^o, 30^o, 45^o and 60^o with the horizontal respectively. The body having the shortest range is? 

At the top of the trajectory of a projectile, the directions of its velocity and acceleration are:

The coordinates of a moving particle at any time ‘t’ are given by x = αt³ and y = βt³. The speed of the particle at time ‘t’ is given by:

1. $\sqrt{{\alpha }^2+{\beta }^2}$

2. $3$ $t\sqrt{{\alpha }^2+{\beta }^2}$

3. $3$ $t^2\sqrt{{\alpha }^2+{\beta }^2}$

4. $t^2\sqrt{{\alpha }^2+{\beta }^2}$