# Formulas of Motion, Brett Morrow

The first law states that every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied. This means that in the nonexistence of a non-zero net force, the focus of mass of a body either remains at rest, or moves at a continuous velocity. The second law states that the relationship between an objects mass (m), it's acceleration (a), and the applied force (F) F=ma. "The property a body has of resisting any change in its state of rest or of uniform motion in a straight line is called inertia. the inertia of a body is related to what can be loosely thought of as the "amount of matter" it contains. A quantitative measure of inertia is mass: the more mass a body has, the less its acceleration when a net force acts on it". The third law states that for every action there is an equal and opposite reaction. The law is sometimes referred to as action-reaction law. Action and Reaction forces never balance out because they act on different bodies. "The first law of motion is included in the second, since a body is not accelerated when there is no net force acting on it and it must therefore remain at rest or in motion at constant velocity. the second and third laws of motion are independent of each other".

# History of Formulas of Motion

Newton's first law is a restatement of the law of inertia which Galileo had already described and Newton gave credit to Galileo. Aristotle had the view that all objects have a natural place in the universe: that heavy objects like rocks wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. He thought that a body was in its natural state when it was at rest, and for the body to move in a straight line at a constant speed an external agent was needed to continually propel it, otherwise it would stop moving. Galileo, however, realized that a force is necessary to change the velocity of a body, i.e., acceleration, but no force is needed to maintain its velocity. This insight leads to Newton's First Law —no force means no acceleration, and hence the body will maintain its velocity.

# Application of Formulas of Motion

Velocity can be expressed as (velocity is constant):
• v = s / t (1a)
• where
• v = velocity (m/s, ft/s)
• s = linear displacement (m, ft)
• t = time (s)
Velocity can be expressed as (acceleration is constant):
• v = v0 + a t (1b)
• where
• v0 = initial linear velocity (m/s, ft/s)
• a = acceleration (m/s2, ft/s2)
Linear displacement can be expressed as (acceleration is constant):
• s = v0 t + 1/2 a t2 (1c)
Combining 1a and 1c to express the final velocity
• v = (v02 + 2 a s)1/2 (1d)
Velocity can be expressed as (velocity is variable)
• v = ds / dt (1f)
• where
• ds = change of displacement (m, ft)
• dt = change in time (s)
Acceleration can be expressed as
• a = dv / dt (1g)
• where
• dv = change in velocity (m/s, ft/s)

# References

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