For the following acceleration versus time graph the corresponding velocity versus displacement graph is: 

1.		2.
3.		4.

The displacement $x$ of a particle moving in one dimension under the action of a constant force is related to time $t$ by the equation $t=\sqrt{x}+3,$ where $x$ is in meters and $t$ is in seconds. What is the displacement of the particle from $t=0~\text s$ to $t = 6~\text s?$

1. $0$
2. $12~\text m$
3. $6~\text m$
4. $18~\text m$

The acceleration $a$ (in ${\mathrm{ms}}^{-2}$) of a body, starting from rest varies with time $t$ (in $\mathrm{s}$) as per the equation $a=3t+4.$ The velocity of the body at time $t=2$ $\mathrm{s}$ will be:

A body thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is:

1. $\sqrt{2}t$

2. $\left(1+\frac{1}{\sqrt{2}}\right)t$

3. $\frac{3t}{2}$

4. $\frac{t}{\sqrt{2}}$

A stone falls freely from rest from a height h and it travels a distance $\frac{9h}{25}$ in the last second. The value of h is:

1. 145 m

2. 100 m

3. 125 m

4. 200 ms

A point moves in a straight line under the retardation $av^2$. If the initial velocity is $u,$ the distance covered in $t$ seconds is:
1. $(aut)$
2. $\frac{1}{a}\mathrm{ln}(aut)$
3. $\frac{1}{a}\mathrm{ln}(1+aut)$
4. $a~\mathrm{ln}(aut)$

A bullet loses $\dfrac{1}{20}$ of its velocity passing through a plank. The least number of planks required to stop the bullet is: (All planks offers same retardation)
1. $10$
2. $11$
3. $12$
4. $23$

A body starts from the origin and moves along the X-axis such that the velocity at any instant is given by $(4t^3-2t)$, where t is in sec and velocity in m/s. What is the acceleration of the particle, when it is 2 m from the origin ?

1. 28 m/s²

2. 22 m/s²

3. 12 m/s²

4. 10 m/s²