Easily Understandable Kinematics

Kinematics is the set of equations and variables used by physicists to predict, understand, and read the motion of an object. It has been a few years for me since I used these equations and principles but I figure I can revisit these topics and document the way I would explain them to someone I was teaching. So what does a good understanding of kinematics require? Well for me the answer to this question would be the position, velocity, acceleration, and time. I will give a list of equations that will allow you to solve for any one of them, and then cover the use of each of these variables.

Equations

Position

The position of the object you are studying is important for the kinematic equations. However, this is only true if this position is relative to a defined axis at a certain time. For example, if one wanted to study movement along the x-axis they would replace x with d in the equations above. Then by rearranging the equations any of the other values could be determined.

Velocity

Velocity is the rate at which position is changing at any particular instance in time. The difference between velocity and speed is velocity comes with a direction. So 30m/s a speed becomes a velocity when making it 30m/s North. Velocity can be found itself by taking the change in location divided by the change in time: v = Δ d/Δ t. In the equations above there are two forms of this v₀ which is the initial velocity(velocity at the start of the time interval) and v or the final velocity.

Acceleration

Acceleration is the rate at which the velocity changes. At any moment in time the acceleration can be found by finding the change in velocity divided by the change in time: a = Δv/Δt, by taking the derivative of the velocity vector, or by solving for it in the equations above.

Time

Lastly there is time. I find this variable to be the one of most importance due to its use in solving for values of any of the other important variables. If the change in time is unknown then you are limited to using the last equation to algebraically solve for it. One last thing I would like to touch on is these equations in multiple dimensions. In this article I will give a summary and finish up in my next post.

Multiple Dimension Kinematics

Once you start to incorporate more than the one axis these equations will take on new forms dependent on the variables and number of axes. For two axes the method of solving for any of the variables above is still similar but now you must solve for each in the x, y, and resultant form. In my next article I will cover this in more detail.