Скачать или смотреть Position, Velocity and Acceleration Equation Explained Visually with Calculus (Physics 1)

In this video we will be going over how calculus is tied to the position formula, velocity formula, and acceleration formula. First lets go over what each fomula is representing…
On this slide I have listed the position or displacement formula which is one half acceleration times time squared plus velocity time time plus initial position. To help visualize this I have a car on the bottom of the slide that is a distance or position of 5 meters from the starting point due to the intial displacement plus 3 meters per unit of time in seconds due to the velocity displacement plus one half 2 meters per time in seconds squared due to the acceleration displacement. I have a graph at the top right which shows how position of the car changes over time using the displayed formula.
The velocity or displacement over time equation is velocity equals acceleration times time plus intial velocity. To illustrate this we can think of a speedometer. We have 2 factors adding to where the location of the dial of the speedometer is. The first is the intial velocity which is 3 m/s then we can add the second factor which is the acceleration or change in velocity over time of 2 m/s/s times time. Plugging in the time we get the velocity value displayed on the speedometer. To the right I have a graph that shows the relationship of the velocity equation over time.
Acceleration is the change of velocity over time. The acceleration formula is acceleration equals acceleration. So acceleration equals 2 m/s/s. This is stating that for every second that passes the velocity will increase by 2 m/s. To the right I have a graph of the acceleration which you can see in this case it remains constant at 2.
Now that we have the equations defined its time to talk calculus. Basically all of these equations are related in that position equations derivative is the velocity equation and the derivative of the velocity equation is the acceleration. Then the anti derivative or integral of acceleration equation is velocity equation and the integral of velocity equation is position equation
Your probably wondering what a derivative is… well is the rate of change or slope or steepness of the line at a given point on one of the graphs on the right. The equation for the slope of the line at a given point of the position formula is the velocity formula the slope of the line at a given point is 2 m/s/s time time plus 3 m/s and the slope of the velocity formula at a given point is the acceleration formula which is 2 m/s
Similarly the anti derivative or integral is the the area under the line that represents the equation or formula. So the area under the acceleration equation is the velocity equation without the unknown constant which is 3 m/s when we don’t know what the constant is we designate it with a plus c Notice that the acceleration times time portion of the velocity equation is that of the rectangle formed by the area under the graph of the acceleration. To take this one step further the area under the velocity equation is the position formula. Notice that the position formula is the formula for a triangle which is ½ base times height which is the acceleration portion plus the formula for a rectangle which is base times height which is the velocity portion.

Disclaimer
These videos are intended for educational purposes only (students trying to pass a class) If you design or build something based off of these videos you do so at your own risk. I am not a professional engineer and this should not be considered engineering advice. Consult an engineer if you feel you may put someone at risk.