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. \(75\ \text{m}\)

A motor car moving with a uniform speed of \(20\ \text{m/s}\) comes to a stop on the application of the brakes after travelling a distance of \(10\ \text{m}\). Its acceleration is:

1. \(20\ \text{m/s}^2\)

2. \(-20\ \text{m/s}^2\)

3. \(-40\ \text{m/s}^2\)

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

The velocity of a body moving with a uniform acceleration of \(2\ \text{m/s}^2\) is \(10\ \text{m/s}\). Its velocity after an interval of \(4\ \text{s}\) is: 

1.  \(12\ \text{m/s}\)
2. \(14\ \text{m/s}\)
3. \(16\ \text{m/s}\)
4. \(18\ \text{m/s}\)

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.