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.

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