A particle starting from rest, moving with constant acceleration, travels a distance \(x\) in first \(2\) seconds and a distance \(y\) in the next two seconds, then: 

1. \(y = x\)

2. \(y = 2x\)

3. \(y = 3x\)

4. \(y = 4x\)

The initial velocity of a body moving along a straight line is \(7\ \text{m/s}\). It has a uniform acceleration of \(4\ \text{m/s}^2\). The distance covered by the body in the \(5^{th}\) second of its motion is:

1. \(25\ \text{m}\)

2. \(35\ \text{m}\)

3. \(50\ \text{m}\)

4. \(85\ \text{m}\)

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.

The position of a particle moving in the XY plane at any time \(t\) is given by \(𝑥 = ( 3 𝑡^ 2 − 6 𝑡 )\) metres. Select the correct statement about the moving particle from the following.

1. The acceleration of the particle is zero at \(t = 0\) second
2. The velocity of the particle is zero at \(t = 0\) second
3. The velocity of the particle is zero at \(t = 1\) second
4. The velocity and acceleration of the particle are never zero

If a body having initial velocity zero is moving with uniform acceleration \(8\ \text{m/s}^2\), then the distance travelled by it in the fifth second will be: 

1. \(36\) metres

2. \(40\) metres

3. \(100\) metres

4. Zero

An alpha particle enters a hollow tube of \(4\ \text{m}\) length with an initial speed of \(1\ \text{km/s}\). It is accelerated in the tube and comes out of it with a speed of \(9\ \text{km/s}\). The time for which it remains inside the tube is:

1. \(8 × 10^{ − 3} \ \text{s}\)

2. \(80 × 10^{ − 3} \ \text{s}\)$\mathrm{ }$

3. \(800 × 10^{ − 3} \ \text{s}\)$\mathrm{}$

4. \(8 × 10^{ − 4} \ \text{s}\)$\mathrm{}$

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. \(d> \dfrac{v^2_1-v^2_2}{2a}\)

A body of mass \(10\ \text{kg}\) is moving with a constant velocity of \(10\ \text{m/s}\). When a constant force acts for \(4\ \text{s}\) on it, it moves with a velocity \(2\ \text{m/s}\) in the opposite direction. The acceleration produced in it is:

1. \(3\ \text{m/s}^2\)
2. \(-3\ \text{m/s}^2\)
3. \(0.3\ \text{m/s}^2\)
4. \(-0.3\ \text{m/s}^2\)