A ball is thrown upward with a certain speed. It passes through the same point at 3 second and 7 second from the start. The maximum height achieved by the ball is:

1.  500 m

2.  250 m

3.  125 m

4.  450 m

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 s to t = 6 s?

1.  0

2.  12 m

3.  6 m

4.  18 m

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

1. 10 ${\mathrm{ms}}^{-1}$

2. 18 ${\mathrm{ms}}^{-1}$

3. 14 ${\mathrm{ms}}^{-1}$

4. 26 ${\mathrm{ms}}^{-1}$

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 a${\mathrm{v}}^2$. If the initial velocity is u, the distance covered in 't' seconds is-

1.  $\mathrm{aut}$

2.  $\frac{1}{\mathrm{a}}\ln \left(\mathrm{aut}\right)$

3.  $\frac{1}{\mathrm{a}}\ln \left(1+\mathrm{aut}\right)$

4.  $\mathrm{a} \ln \left(\mathrm{aut}\right)$

A particle is thrown upwards from ground. It experiences a constant resistance force which can produce retardation of 2 $m/s^2$. The ratio of time of ascent to the time of descent is: $[g=10 m/s^2]$

(1) 1:1

(2) $\sqrt{\frac{2}{3}}$

(3) $\frac{2}{3}$

(4) $\sqrt{\frac{3}{2}}$

A bullet loses $\frac{1}{20}$ 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