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.  \(500\text{ m}\)

2.  \(250\text{ m}\)

3.  \(125\text{ m}\)

4.  \(450\text{ m}\)

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

1.		2.
3.		4.

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 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 point moves with uniform acceleration and v₁, v₂ and v₃ denote the average velocities in the three successive intervals of time t₁, t₂ and t₃. Which of the following relations is correct ?

1. $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_2+t_3)$

2. $(v_1-v_2):(v_2-v_3)=(t_1+t_2):(t_2+t_3)$

3. $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_1-t_3)$

4. $(v_1-v_2):(v_2-v_3)=(t_1-t_2):(t_2-t_3)$ 

The initial velocity of the particle is 10 m/sec and its retardation is 2 m/sec². The distance moved by the particle in 5^th second of its motion is 

1. 1 m

2. 19 m

3. 50 m

4. 75 m

A motor car moving with a uniform speed of 20 m/sec comes to stop on the application of brakes after travelling a distance of 10 m. Its acceleration is 

1. 20 m/sec²

2. –20 m/sec²

3. –40 m/sec²

4. +2 m/sec²

The velocity of a body moving with a uniform acceleration of 2 m/sec² is 10 m/sec. Its velocity after an interval of 4 sec is 

1. 12 m/sec

2. 14 m/sec

3. 16 m/sec

4. 18 m/sec