When a ball of mass \(5\ \text{kg }\)hits a bat with a velocity \(3\ \text{m/s}\), in the positive direction, and it moves back with a velocity \(4\ \text{m/s}\). The impulse in SI units is:

1. \(5 \)

2. \(15\)

3. \(25\)

4. \(35\)

A particle of mass \(m\) has momentum \(p\). Its kinetic energy will be:
1. \(mp\)
2.  \(p^2 𝑚\)
3.  \(\dfrac{𝑝^ 2}m\)
4.  \(\dfrac{𝑝^ 2}{2m}\)

A particle of mass 15 kg has an initial velocity \(\vec{v}_i=\hat{i}-2\hat{j}\ \text{m/s}\). It collides with another body, and the impact time is \(0.1\ \text{s}\), resulting in a velocity \(\vec{v}_f=6\hat{i}+4\hat{j}+5\hat{k}\ \text{m/s}\) after impact. The average force of impact on the particle is:

1. \(15\left(5\hat{i}+6\hat{j}+5\hat{k}\right)\)
2.  \(15\left(5\hat{i}+6\hat{j}-5\hat{k}\right)\)
3. \(150\left(5\hat{i}-6\hat{j}+5\hat{k}\right)\)
4. \(150\left(5\hat{i}+6\hat{j}+5\hat{k}\right)\)

A particle of mass \(m\) at rest is acted upon by a constant force \(F\) for a time \(t\). Its kinetic energy after an interval \(t\) is:

1. \(\dfrac{F^2t^2}{m}\)

2. \(\dfrac{F^2t^2}{2m}\)

3. \(\dfrac{F^2t^2}{3m}\)

4. \(\dfrac{Ft}{2m}\)

The magnitude of the impulse developed by a mass of 0.2 kg which changes its velocity from \(\vec{v}_i=5\hat{i}-3\hat{j}+7\hat{k}\ \text{m/s}\)  to \(\vec{v}_f=2\hat{i}+3\hat{j}+\hat{k}\ \text{m/s}\) is: 
1. \(2.7\ \text{N-s}\)
2. \(1.8\ \text{N-s}\)
3. \(0.9\ \text{N-s}\)
4. \(3.6\ \text{N-s}\)