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 is thrown vertically up to reach its maximum height in \(t\) seconds. The total time from the time of projection to reach a point at half of its maximum height while returning (in seconds) is:

1. \(\sqrt2\ t\)

2. \(\left(1+\dfrac{1}{\sqrt2}\right)t\)

3. \(\dfrac{3t}{2}\)

4. \(\dfrac{t}{\sqrt2}\)

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. \(200 \ \text{m}\)

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 velocity of a body depends on time according to the equation \(𝑣 = 20 + 0 .1 \ 𝑡^ 2\). The body is undergoing:

1. Uniform acceleration

2. Uniform retardation

3. Non-uniform acceleration

4. Zero acceleration

Which of the following four statements is false?

1. A body can have zero velocity and still be accelerated.

2. A body can have a constant velocity and still have a varying speed.

3. A body can have a constant speed and still have a varying velocity.

4. The direction of the velocity of a body can change when its acceleration is constant.

Two cars \(A\) and \(B\) are travelling in the same direction with velocities \(v_1\) and \(v_2 (v_1>v_2)\). 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. \(d< \dfrac{(v_1-v_2)^2}{2a}\)

2. \(d< \dfrac{v^2_1-v^2_2}{2a}\)

3. \(d> \dfrac{(v_1-v_2)^2}{2a}\)

4. \(d> \dfrac{v^2_1-v^2_2}{2a}\)

The displacement of a particle is given by \(y = a + bt + ct^{2} - dt^{4}\). The initial velocity and acceleration are, respectively:

Two trains travelling on the same track are approaching each other with equal speeds of \(40\ \text{m/s}\). The drivers of the trains begin to decelerate simultaneously when they are just \(2.0\ \text{km}\) apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be:

1. \(11.8\ \text{m/s}^2\)
2. \(11.0\ \text{m/s}^2\)
3. \(1.6\ \text{m/s}^2\)
4. \(0.8\ \text{m/s}^2\)