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

1. displacement is $2\pi \mathrm{R.}$

2. distance covered is 2R.

3. displacement is zero.

4. distance covered is zero.

A person, reaches a point directly opposite on the other bank of a flowing river, while swimming at a speed of 5 m/s at an angle of $120°$ with the flow. The speed of the flow must be

1. 2.5 m/s

2. 3 m/s

3. 4 m/s

4. 1.5 m/s

A car with a vertical windshield moves in a rain storm at a speed of 40 km/hr. The rain drops fall vertically with a constant speed of 20 m/s. The angle at which raindrops strike the windshield is

1. ${\tan }^{-1}\frac{5}{9}$

2. ${\tan }^{-1}\frac{9}{5}$

3. ${\tan }^{-1}\frac{3}{2}$

4. ${\tan }^{-1}\frac{2}{3}$

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

A car is moving at a speed of 40 m/s on a circular track of radius 400 m. This speed is increasing at the rate of 3 m/s². The acceleration of the car is

1. 4 m/s²

2. 7 m/s²

3. 5 m/s²

4. 3 m/s²

A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio of $\frac{\mid \text{ displacement }\mid }{\text{ distance }}$ will be

1. 0

2. $\frac{1}{7}$

3. $\frac{2}{7}$

4. $\frac{1}{11}$