Equation of motion: All of the below ordinary differential equations (ODES) describe motion subjected to different forcing functions: In all cases, the velocity v is the dependent variable and time I is the independent variable. In all cases, for simplicity let m = 1 kg and F = 10 N unless otherwise noted. For background reading, Chapter 2.1-2.6 covers objects in a gravitational field and solution through separation of variables. Note that a gravitational field is at the same thing as a constant forcing function. In this case F = mg. Chapter 3.2 and 3.3 gives the definition of a linear ODE and the method of the integration factor for first order, linear ODES. For each of these equations, answer the following questions:
Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
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