A stone falls freely from rest from a height \(h\) and it travels a distance \(\dfrac{9h}{25}\) in the last second. The value of \(h\) is: (Take \(g=10\ \text{m/s}^2\))

1. \(145\ \text{m}\)

2. \(100\ \text{m}\)

3. \(125\ \text{m}\)

4. \(200 \ \text{m}\)

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

2. \(\dfrac{1}{a}\mathrm{ln}(aut)\)

3. \(\dfrac{1}{a}\mathrm{ln}(1+aut)\)

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 \( ( 4 𝑡^ 3 − 2 𝑡 )\), where \(t\) is in sec and velocity in m/s. What is the acceleration of the particle when it is \(2\ \text{m}\) from the origin?

1. \(28\ \text{m/s}^2\)

2. \(22\ \text{m/s}^2\)

3. \(12\ \text{m/s}^2\)

4. \(10\ \text{m/s}^2\)

The relation between time and distance is given by $$\(t=\alpha x^2+\beta x,\) where \(\alpha\) and \(\beta\) are constants. The retardation, as calculated based on this equation, will be (assume \(v\) to be velocity):
1. $\mathrm{}$\(2\alpha v^3\)
2. \(2\beta v^3\)$\mathrm{}{\mathrm{}}^{}$
3. \(2\alpha\beta v^3\)$\mathrm{}{\mathrm{}}^{}$
4. \(2\beta^2 v^3\)$\mathrm{}{\mathrm{}}^{}$

A point moves with uniform acceleration, and \(v_1,\ v_2\) and \(v_3\) denote the average velocities in the three successive intervals of time \(t_1,\ t_2\) and \(t_3\). 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. \((v_1 - v_2):(v_2 - v_3) = (t_1 - t_2):(t_2 - t_3)\)
4. \((v_1 - v_2):(v_2 - v_3) = (t_1 + t_2):(t_2 - t_3)\) 

The acceleration of a moving body can be found from: 

1. Area under the velocity-time graph

2. Area under the distance-time graph

3. Slope of the velocity-time graph

4. Slope of the distance-time graph

The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid 

1. $v=u+a{t}^2$

2. $v=u+a\frac{t^2}{2}$

3. $v=u+at$

4. v = u

The initial velocity of the particle is \(10\ \text{m/s}\) and its retardation is \(2\ \text{m/s}^2\). The distance moved by the particle in \(5^{th}\) second of its motion is:

1. \(1\ \text{m}\)
2. \(19\ \text{m}\)
3. \(50\ \text{m}\)
4. \(75\ \text{m}\)