A particle moves along a path \(ABCD\) as shown in the figure. The magnitude of the displacement of the particle from \(A\) to \(D\) is:

       

1. $(5+10\sqrt{2})$m
2. \(10\) m
3. $15\sqrt{2}$ m
4. \(15\) m

Which of the following four statements is false?

Two cars A and B are travelling in the same direction with velocities v₁ and v₂ $(v_1>v_2)$. When the car A is at a distance d behind car B, the driver of the car A applied the brake producing uniform retardation a. There will be no collision when-

1. $d<\frac{{(v_1-v_2)}^2}{2a}$

2. $d<\frac{v_1^2-v_2^2}{2a}$

3. $d>\frac{{(v_1-v_2)}^2}{2a}$

4. $d>\frac{v_1^2-v_2^2}{2a}$ 

A particle moves a distance x in time t according to equation x = (t+5)^-1. The acceleration of the particle is proportional to: 

The position x of a particle moving along the x-axis varies with time t as x = $20\mathrm{t}$ $-$ $5{\mathrm{t}}^2$, where x is in meters and t is in seconds. The particle reverses its direction of motion at:

1. x = 40 m

2. x = 10 m

3. x = 20 m

4. x = 30 m

A body starting from rest moves with uniform acceleration on a horizontal surface. The body covers 3 consecutive equal distances from the beginning in time ${\mathrm{t}}_1,$ ${\mathrm{t}}_2 , \mathrm{and}$ ${\mathrm{t}}_3$ seconds. The ratio of ${\mathrm{t}}_1:{\mathrm{t}}_2:{\mathrm{t}}_3$ is:
1. 1: 2 : 3
2. $1:\sqrt{2}:\sqrt{3}$
3. $1:(\sqrt{2}-1):(\sqrt{3}-\sqrt{2})$
4. $\sqrt{3}:\sqrt{2}:1$

The position (x) of a particle in a straight line motion is given by $\mathrm{x}=2+10\mathrm{t}-5{\mathrm{t}}^2$ $\left(\mathrm{m}\right)$. Its velocity (v) is best represented by?

1.		2.
3.		4.

An elevator whose floor to ceiling height is 12 meters, moves upward with an acceleration of $2.2$ $\mathrm{m}/{\mathrm{s}}^2$. After 1.5 seconds since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is

1. 1 s

2. 2 s

3. $\sqrt{2}$ s

4. $\sqrt{3}$ s

The displacement \((x)\) of a point moving in a straight line is given by; \(x=8t^2-4t.\) Then the velocity of the particle is zero at:

The velocity v of an object varies with its position x on a straight line as $\mathrm{v}=3\sqrt{\mathrm{x}}$. Its acceleration versus time (a-t) graph is best represented by:

1.		2.
3.		4.