Answer
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(a) The particle model is just a way for us to visualise an object's motion if all of its mass is concentrated at a single point at a specific time.
(b) A couple of simple examples of situations where the particle model may be useful are a baseball being thrown by a pitcher to the catcher. We would treat the baseball as the particle, and we could display it's position as a function of time with the particle model. Another good application would be a person running on a track. The runner would be our particle, and we could map their position as a function of time fairly easily.
(c)The particle model is not ideal for any object that is stationary or is experiencing rotational motion ONLY. One example of this would be a ceiling fan. While the ceiling fan is moving, it isn't changing it's position and a particle model would do us no good in that scenario.