Physics of Motion

What Formulas Do We Use When Calculating Motion?

When it comes to solving for any of these variables, we have five main equations that we can use:

The first is given as

$∆x=vt$

This is the most simple formula, meaning that distance is equal to speed multiplied by time, only taking into account direction as well. This can only be used when acceleration is equal to 0.

The second equation is one of the three kinematic equations. Note that it does not depend on position.

$v=v_0+at$

Where$v$is the final velocity of an object,$v_0$is its starting velocity,$a$is the acceleration acting on it, and$t$is the time that passes during motion.

Our third equation is another kinematic equation. This time it does not depend on the final velocity.

$∆x=\left(v_{0}t\right)+\frac{1}{2}{\left(at\right)}^2$

Where $\text{∆x}$ is the displacement. This formula can only be used if the acceleration on the object is positive.

Our fourth equation below is an easier way to calculate displacement when you know both the starting and final velocities that act on the object.

$∆x=\frac{1}{2}(v_0+v)t$

And our last equation is also the final kinematic equation. Note it does not depend on time :

$v^2={v_0}^2+2a∆x$

Using these equations, we can solve for any particular variable we need to when studying an object in motion.

What Are the Laws of Motion?

The laws defining the behavior of motion were first discovered and written by English physicist Sir Isaac Newton, and they apply to almost everything in the universe.

First Law: Law of Intertia

In simple terms, the first law of motion states that objects that are not being pushed will eventually come to rest. This means that if an object is experiencing no change in the forces acting on it, the object will tend towards a state of no movement, or rest.

Second Law: F = ma

The second law of motion shows us that rate of change of the momentum of an object is exactly the same as the force that is being applied to it. In other words, if an object has a mass of$m,$the force acting on it is equal to its mass multiplied by its acceleration. This can be written as $F=ma.$

Third Law: Action & Reaction

The main way this law has been stated in the past is that every action has an equal and opposite reaction. This isn’t quite true, or just not quite informative enough. The third law of motion states that when two objects are to come into contact with each other, the forces that are applied to one another are equal in magnitude and opposite in direction.

For example, if an object is laying on the ground, the object is pushing down on the ground with its weight, which we know is a force. As we know of the third law of motion, we know that the ground is also pushing back, with a force equal to the weight and in the exact opposite direction.

What Are the Types of Motion?

Movement occurs in a multitude of different ways, and the forces that are applied to objects in these different states of movement vary greatly. Here are a few types of motion:

Linear Motion

Linear motion is straightforward, as it describes any form of movement that occurs in a straight line. This is the most basic form of motion. Nothing special or complicated has to occur when traveling from point A to point B.

Oscillating Motion

Oscillating motion is a back and forth movement. Only when this movement is consistent over time can it be considered an oscillating motion. Waves, including sound waves, ocean waves, and radio waves are examples of oscillating motion. Waves use oscillating motion to store information in their amplitudes. Other common examples of oscillating motion are pendulums and springs.

A spring is a great example of an oscillating motion, Wikimedia Commons

Rotary Motion

Rotary motion will move in a circular pattern. The use of this motion has been incredibly beneficial to use over time, with the use of the wheel to transport things, as well as many other real-world examples.

A diagram of rotary motion, showing the direction of velocity and acceleration. Brews ohare CC BY-SA 3.0

Projectile Motion

Projectile motion is the movement of any object when thrown in an environment containing a gravitational field. If an object is thrown higher than horizontally, then the path it travels will form a curve, known as a parabola.