Which one of the following is not true?

1.	The net acceleration of a particle in a circular motion is always along the radius of the circle towards the center.
2.	The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point.
3.	The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector.
4.	None of the above.

A particle starts from the origin at t = 0 sec with a velocity of $10$ $\hat{j}$ $m/s$ and moves in the x-y plane with a constant acceleration of \((8.0\hat i +2.0 \hat j)\) \(\text{ms}^{-2}\). At what time is the x- coordinate of the particle 16 m?

For any arbitrary motion in space, which of the following relations is true?

A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of \(|displacement| \over distance\) will be:
1. 0
2. 1/7
3. 2/7
4. 1/11

Consider the motion of the tip of the second hand of a clock. In one minute (assuming \(R\) to be the length of the second hand), its:

A particle projected from origin moves in the x-y plane with a velocity $\overrightarrow{\mathrm{v}}=3\hat{\mathrm{i}}+6\mathrm{x}\hat{\mathrm{j}}$, where $\hat{\mathrm{i}}$ and $\hat{\mathrm{j}}$ are the unit vectors along the x and y-axis. The equation of path followed by the particle is:

1. $\mathrm{y}={\mathrm{x}}^2$

2. $\mathrm{y}=\frac{1}{{\mathrm{x}}^2}$

3. $\mathrm{y}=2{\mathrm{x}}^2$

4. $\mathrm{y}=\frac{1}{\mathrm{x}}$

The position coordinates of a projectile projected from ground on a certain planet (with no atmosphere) are given by $\mathrm{y}=(4\mathrm{t}-2{\mathrm{t}}^2)\mathrm{m}$ and $\mathrm{x}=\left(3\mathrm{t}\right)$ metre, where t is in seconds and point of projection is taken as the origin. The angle of projection of projectile with vertical is:

1. $30°$

2. $37°$

3. $45°$

4. $60°$

The velocity at the maximum height of a projectile is $\frac{\sqrt{3}}{2}$ times its initial velocity of projection (u). Its range on the horizontal plane is:

1. $\frac{\sqrt{3}{\mathrm{u}}^2}{2\mathrm{g}}$

2. $\frac{3{\mathrm{u}}^2}{2\mathrm{g}}$

3. $\frac{3{\mathrm{u}}^2}{\mathrm{g}}$

4. $\frac{{\mathrm{u}}^2}{2\mathrm{g}}$

The equation of a projectile is $\mathrm{y}=\mathrm{ax}-{\mathrm{bx}}^2$. Its horizontal range is?

1. $\frac{\mathrm{a}}{\mathrm{b}}$

2. $\frac{\mathrm{b}}{\mathrm{a}}$

3. $\mathrm{a}+\mathrm{b}$

4. $\mathrm{b}-\mathrm{a}$

When a particle is projected at some angle to the horizontal, it has a range R and time of flight t₁. If the same particle is projected with the same speed at some other angle to have the same range, its time of flight is t₂, then:

1. ${\mathrm{t}}_1+{\mathrm{t}}_2=\frac{2\mathrm{R}}{\mathrm{g}}$

2. ${\mathrm{t}}_1-{\mathrm{t}}_2=\frac{\mathrm{R}}{\mathrm{g}}$

3. ${\mathrm{t}}_1{\mathrm{t}}_2=\frac{2\mathrm{R}}{\mathrm{g}}$

4. ${\mathrm{t}}_1{\mathrm{t}}_2=\frac{\mathrm{R}}{\mathrm{g}}$