When a ball of mass = 5kg hits a bat with a velocity = 3 m/s, in positive direction and it moves back with a velocity = 4 m/s, find the impulse in SI units

1. 5 

2. 15

3. 25

4. 35

A particle of mass m has momentum p. it's kinetic energy will be 

1.  mp

2.  $p^{2}m$

3.  $\frac{p^2}{m}$

4.  $\frac{p^2}{2m}$

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

1.  $15\left|5\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 5\hat{\mathrm{k}}\right|$

2.  $15\left|5\hat{\mathrm{i}} + 6\hat{\mathrm{j}} - 5\hat{\mathrm{k}}\right|$

3.  $150\left|5\hat{\mathrm{i}} - 6\hat{\mathrm{j}} + 5\hat{\mathrm{k}}\right|$

4.  $150\left|5\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 5\hat{\mathrm{k}}\right|$

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.  $\frac{{\mathrm{F}}^2{\mathrm{t}}^2}{\mathrm{m}}$

2.  $\frac{{\mathrm{F}}^2{\mathrm{t}}^2}{2\mathrm{m}}$

3.  $\frac{{\mathrm{F}}^2{\mathrm{t}}^2}{3\mathrm{m}}$

4.  $\frac{\mathrm{Ft}}{2\mathrm{m}}$

The magnitude of the impulse developed by a mass of 0.2 kg which changes its velocity from $5\hat{\mathrm{i}} - 3\hat{\mathrm{j}} + 7\hat{\mathrm{k}} \mathrm{m}/\mathrm{s} \mathrm{to} 2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} + \hat{\mathrm{k}} \mathrm{m}/\mathrm{s}$ is

1.  2.7 N-s

2.  1.8 N-s

3.  0.9 N-s

4.  3.6 N-s